{"title":"Wolfgang Hackbusch","description":null,"products":[{"product_id":"multigrid-methods-ii-book-wolfgang-hackbusch-9783540171980","title":"Multigrid Methods II","description":null,"brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52130813575441,"sku":"NLS9783540171980","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783540171980.jpg?v=1785898739"},{"product_id":"multi-grid-methods-and-applications-book-wolfgang-hackbusch-9783540127611","title":"Multi-Grid Methods and Applications","description":"Multi-grid methods are the most efficient tools for solving elliptic boundary value problems. One section describes special applications (convection-diffusion equations, singular perturbation problems, eigenvalue problems, etc.).","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52139805671697,"sku":"NLS9783540127611","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":52761568411921,"sku":"NIN9783540127611","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783540127611.jpg?v=1785823217"},{"product_id":"integral-equations-book-wolfgang-hackbusch-9783764328719","title":"Integral Equations","description":"The theory of integral equations has been an active research field for many years and is based on analysis, function theory, and functional analysis. On the other hand, integral equations are of practical interest because of the boundary integral equation method, which transforms partial differential equations on a domain into integral equations over its boundary. This book grew out of a series of lectures given by the author at the Ruhr-Universitat Bochum and the Christian-Albrecht-Universitat zu Kiel to students of mathematics. The contents of the first six chapters correspond to an intensive lecture course of four hours per week for a semester. Readers of the book require background from analysis and the foundations of numeri- cal mathematics. Knowledge of functional analysis is helpful, but to begin with some basic facts about Banach and Hilbert spaces are sufficient. The theoretical part of this book is reduced to a minimum; in Chapters 2, 4, and 5 more importance is attached to the numerical treatment of the integral equations than to their theory. Important parts of functional analysis (e. g., the Riesz-Schauder theory) are presented without proof. We expect the reader either to be already familiar with functional analysis or to become motivated by the practical examples given here to read a book about this topic. We recall that also from a historical point of view, functional analysis was initially stimulated by the investigation of integral equations.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52143402287377,"sku":"NLS9783764328719","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783764328719.jpg?v=1786095941"},{"product_id":"elliptic-differential-equations-book-wolfgang-hackbusch-9783662549605","title":"Elliptic Differential Equations","description":"This book offers a simultaneous treatment of the theory and the numerical treatment of elliptic problems. The subjects dealt with include the classical theory (Green's function, maximum principle, etc.) as well as the variational formulation. The author describes and analyses finite difference and finite element methods. Specific chapters are devoted to the eigenvalue problem and the Stokes problem.","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52348116697361,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52348120596753,"sku":"NLS9783662549605","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783662549605.jpg?v=1785806349"},{"product_id":"incomplete-decomposition-ilu-algorithms-theory-and-applications-book-wolfgang-hackbusch-9783528076412","title":"Incomplete Decomposition (ILU) — Algorithms, Theory, and Applications","description":"This volume contains 22 papers presented at the Kiel Seminar in 1992. The Kiel Seminars are well known, and cover special areas in numerical methods for partial differential equations, numerical linear algebra, numerical methods for integral equations and related areas. The papers cover a broad range of topics from mathematical theory to practical applications of incomplete decompositions as smoothers in multi-grid methods, as preconditioners for conjugate gradient-type methods and the use of ILU for systems of partial differential equations.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52405684371729,"sku":"NLS9783528076412","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783528076412.jpg?v=1785761043"},{"product_id":"integralgleichungen-book-wolfgang-hackbusch-9783519023708","title":"Integralgleichungen","description":"Die Integralgleichungen stellen ein Gebiet dar. das f r sich durchaus selbst ndig ist und auf einer interessanten Mischung von Analysis. Funktionentheorie und Funktionalanalysis beruht. Auf der anderen Seite gewinnen die Integralgleichungen ihr praktisches Interesse aus der Integralgleichungsmethode. die es erlaubt, partielle Differential- gleichungen in Integralgleichungen umzuformen. Das Buch ist aus Vorlesungen hervorgegangen, die der Autor an der Ruhr-Universit t Bochum und der Christian-Albrechts-Universit t Kiel gehalten hat. Der Umfang der Kapitel 1 bis 6 entspricht etwa einer intensiven vierst ndigen Vorlesung. Das Studium der Integral- gleichungen kann mit Vorkenntnissen der Analysis und den Grundlagen der Numerik aufgenommen werden. Kenntnisse aus der Funktional- analysis sind hilfreich. aber nicht unabdingbar, wenn Grundbegriffe wie Banach-und Hilbert-R ume gel ufig sind. Der Theorieteil dieses Buches ist so knapp wie m glich bemessen. da die Numerik in den Kapiteln 2. 4, 5 im Vordergrund stehen soll. Wichtige Teile der ben tigten Funktionalanalysis wie etwa die Riesz-Schauder-Theorie werden ohne Herleitung wiedergegeben. Es wird dabei davon ausgegangen. da  dem Leser dieses Gebiet entweder aus einer Vorlesung  ber Funktionalanalysis bekannt ist oder da  e- mit gesteigerter Motivation durch praktische Beispiele - diese Kapitel durch Vorlesungen oder Lekt re nachholen wird. Es sei daran erinnert. da  auch historisch die Funktionalanalysis aus der Diskussion der Integralgleichungen hervorgegangen ist. Als Funktionenr ume werden in dieser Darstellung vornehmlich die klassischen der stetigen oder H lder-stetigen Funktionen verwendet. Die Sobolev-R ume werden weitgehend vermieden. was zum Beispiel zur Folge hat. da  die Integraloperatoren hier nicht in der erforderlichen Allgemeinheit als Pseudodifferentialoperatoren diskutiert werden k nnen.","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52409029329169,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52409039946001,"sku":"NLS9783519023708","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783519023708.jpg?v=1790161116"},{"product_id":"fast-solvers-for-flow-problems-book-wolfgang-hackbusch-9783528076498","title":"Fast Solvers for Flow Problems","description":"This volume contains 23 contributions to the 10th GAMM-Seminar, which was held in Kiel on the 14-16 of January 1994. The central topics are advanced numerical techniques for solving flow problems. The Navier-Stokes equations are discussed with respect to anisotropically refined meshes, in combination with non-equilibrium chemistry and with respect to implicit time-discretizations and parallel solvers. Furthermore, robust multi-grid methods are described for this problem. Five papers are devoted to parallel algorithms, and a further one to domain decomposition techniques. The very important aspect of adaptive strategies is considered in several contributions, including a discussion of appropriate error estimators. Other subjects are the FEM-BEM coupling, convection-dominated systems, unstructured grid techniques and complex geometries in 3-D.","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52409814581521,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52409815138577,"sku":"NLS9783528076498","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783528076498.jpg?v=1786791604"},{"product_id":"numerical-treatment-of-the-navier-stokes-equations-book-wolfgang-hackbusch-9783528076306","title":"Numerical Treatment of the Navier-Stokes Equations","description":"The most frequently used method for the numerical integration of parabolic differential equa- tions is the method of lines, where one first uses a discretization of space derivatives by finite differences or finite elements and then uses some time-stepping method for the the solution of resulting system of ordinary differential equations. Such methods are, at least conceptually, easy to perform. However, they can be expensive if steep gradients occur in the solution, stability must be controlled, and the global error control can be troublesome. This paper considers a simultaneaus discretization of space and time variables for a one-dimensional parabolic equation on a relatively long time interval, called 'time-slab'. The discretization is repeated or adjusted for following 'time-slabs' using continuous finite element approximations. In such a method we utilize the efficiency of finite elements by choosing a finite element mesh in the time-space domain where the finite element mesh has been adjusted to steep gradients of the solution both with respect to the space and the time variables. In this way we solve all the difficulties with the classical approach since stability, discretization error estimates and global error control are automatically satisfied. Such a method has been discussed previously in  3] and  4]. The related boundary value techniques or global time integration for systems of ordinary differential equations have been discussed in several papers, see  12] and the references quoted therein.","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52409856655633,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52409857343761,"sku":"NLS9783528076306","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783528076306.jpg?v=1789124943"},{"product_id":"numerical-techniques-for-boundary-element-methods-book-wolfgang-hackbusch-9783528076337","title":"Numerical Techniques for Boundary Element Methods","description":"11 The GAMM Committee for Efficient Numerical Methods for Partial 11 Differential Equations organises workshops on subjects concerning the algorithmic treatment of partial differential equations. The topics are discretisation methods like the finite element and the boundary element method for various types of applications in structural and fluid mechanics. Particular attention is devoted to the advanced solution methods. The series of such workshops was continued in 1991, January 25- 27, with the 7th Kiel-Seminar on the special topic 11 11 Numerical techniques for boundary element methods at the Christian-Albrechts-University of Kiel. The seminar was attended by 57 scientists from 8 countries. The list of topics contained applications of the boundary element method (BEM) to various problems of practical interest, algo- rithmic aspects of the BEM (coupling with finite element method, parallelisation), convergence analysis, and in particular the treatment of the numerical integration. In six contributions the quadrature of weakly singular, Cauchy singular, and hypersingular integrals is analysed. 11 11 The editor thanks the DFG-Schwerpunkt Randelementmethoden for its support. He also likes to express his gratitude to all persons involved in the organisation of the seminar.","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52410138329361,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52410138886417,"sku":"NLS9783528076337","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783528076337.jpg?v=1758776908"},{"product_id":"integralgleichungen-book-wolfgang-hackbusch-9783519123705","title":"Integralgleichungen","description":"Die Integralgleichungen stellen ein Gebiet dar. das f r sich durchaus selbst ndig ist und auf einer interessanten Mischung von Analysis. Funktionentheorie und Funktionalanalysis beruht. Auf der anderen Seite gewinnen die Integralgleichungen ihr praktisches Interesse aus der Integralgleichungsmethode. die es erlaubt, partielle Differential- gleichungen in Integralgleichungen umzuformen. Das Buch ist aus Vorlesungen hervorgegangen, die der Autor an der Ruhr-Universit t Bochum und der Christian-Albrechts-Universit t Kiel gehalten hat. Der Umfang der Kapitel 1 bis 6 entspricht etwa einer intensiven vierst ndigen Vorlesung. Das Studium der Integral- gleichungen kann mit Vorkenntnissen der Analysis und den Grundlagen der Numerik aufgenommen werden. Kenntnisse aus der Funktional- analysis sind hilfreich. aber nicht unabdingbar, wenn Grundbegriffe wie Banach-und Hilbert-R ume gel ufig sind. Der Theorieteil dieses Buches ist so knapp wie m glich bemessen. da die Numerik in den Kapiteln 2. 4, 5 im Vordergrund stehen soll. Wichtige Teile der ben tigten Funktionalanalysis wie etwa die Riesz-Schauder-Theorie werden ohne Herleitung wiedergegeben. Es wird dabei davon ausgegangen. da  dem Leser dieses Gebiet entweder aus einer Vorlesung  ber Funktionalanalysis bekannt ist oder da  e- mit gesteigerter Motivation durch praktische Beispiele - diese Kapitel durch Vorlesungen oder Lekt re nachholen wird. Es sei daran erinnert. da  auch historisch die Funktionalanalysis aus der Diskussion der Integralgleichungen hervorgegangen ist. Als Funktionenr ume werden in dieser Darstellung vornehmlich die klassischen der stetigen oder H lder-stetigen Funktionen verwendet. 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As is well known these methods can converge very fast on problems with a smooth solution and a regular mesh, but the rate of convergence can be severely degraded for problems with unisotropy or discontinuous coefficients unless some form of robust smoother is used. Also problems can arise with the increasingly coarser meshes because for some types of discretization methods, coercivity may be lost on coarse meshes and on massively parallel computers the computation cost of transporting information between computer processors devoted to work on various levels of the mesh can dominate the whole computing time. For discussions about some of these problems, see (11). Here we propose a method that uses only two levels of meshes, the fine and the coarse level, respec- tively, and where the corrector on the coarse level is equal to a new type of preconditioner which uses an algebraic substructuring of the stiffness matrix. It is based on the block matrix tridiagonal structure one gets when the domain is subdivided into strips. This block-tridiagonal form is used to compute an approximate factorization whereby the Schur complements which arise in the recursive factorization are approximated in an indirect way, i. e.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52410848903441,"sku":"NLS9783528080976","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":53015419912465,"sku":"NIN9783528080976","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783528080976.jpg?v=1758780178"},{"product_id":"iterative-losung-groer-schwachbesetzter-gleichungssysteme-book-wolfgang-hackbusch-9783519123729","title":"Iterative Lösung großer schwachbesetzter Gleichungssysteme","description":"4 Die aus der Linearen Algebra ben tigten Grundlagen sind noch einmal in Kapitel 2 dieses Buches zusammengestellt. Damit soll zum einen eine geschlossene Darstellung erm glicht werden, zum anderen ist es notwendig, die aus der Linearen Algebra bekannten S tze in die hier ben tigte Formulierung zu bringen. Vom Umfang her eignet sich eine Auswahl des vorliegenden Stoffes fUr eine 4-st ndige Vorlesung nach dem Vordiplom. Eine Teilauswahl ist auch f r die Vorlesung Numerische MathematikII empfehlenswert. Die aufgef hrten  bungsaufgaben, die auch als Bemerkungen ohne Beweis verstanden werden k nnen, sind in die Darstellung integriert. Wird dieses Buch als Grundlage einer Vorlesung benutzt, k nnen sie als  bungen dienen. Aber auch der Leser sollte versuchen, sein Verst ndnis der Lekt re an den Aufgaben zu testen. Die Diskussion der Verfahren ist durch zahlreiche numerische Bei- spiele zumeist anhand des Poisson-Modellproblems illustriert. Damit der interessierte Leser die Verfahren mit anderen Parametern, Schritt- weiten etc. testen kann, sind die Verfahren auch explizit als Pascal- Programme angegeben. Die Sammlung der Quelltexte ist als Diskette erh ltlich (siehe  Prog1 im Literaturverzeichnis und Bestellformular auf den Seiten 38112). Diese Programmsammlung k nnte auch unabh ngig vom Buch zur Unterst tzung von Vorlesungen oder Seminaren mit numerischen Beispielen herangezogen werden. Der Autor dankt seinen Mitarbeitern, insbesondere Herrn J. Bur- meister f r Literaturrecherchen und die Unterst tzung beim Lesen und Korrigieren des Manuskriptes. Diskussionen mit den Kollegen Niethammer, Mae , Dry ja, Wittum, u.a. verdanke ich viele Anregungen und Literaturhinweise. Dem Teubner-Verlag gilt der Dank f r die stets freundliche Zusammenarbeit.","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52426940875025,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52426941301009,"sku":"NLS9783519123729","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783519123729.jpg?v=1786091877"},{"product_id":"theorie-und-numerik-elliptischer-differentialgleichungen-book-wolfgang-hackbusch-9783658153571","title":"Theorie und Numerik elliptischer Differentialgleichungen","description":"Dieses Buch ist aus Vorlestmgen entstanden, die der Autor an der Ruhr-Universitiit Bochum und an der Christian-Albrechts-Universitiit Kiel fUr Studenten der Mathematik gehalten hat. Die vorliegende Abhandltmg beschriinkt sich auf partielle Differentialgleichtmgen yom ell i p tis c hen Typ, da andemfalls die Darstelltmg entweder zu oberfliichlich oder zu umfangreich geriete. Die folgende Skizze zeigt, welche Aufgaben sich bei elliptischen Differentialgleichungen ergeben. A: Theorie der B: Diskretisierungen C: Numerische Analyse: elliptischen (Differenzenverfahren, Konvergenz, Gleichtmgen finite Elemente, etc) Stabilitiit elliptische diskrete Gleichung ---------------- Randwertaufgabe i D: Gleichungsauflbsung E: Theorie der a) direkt oder durch Iterationsverfahren b) I terationsverfahren Die The 0 r i e der elliptischen Gleichtmgen (A) beschiiftigt sich mit den Fragen nach Existenz, Eindeutigkeit und Eigenschaften der Lbsung. Das erste Problem der Numerik ist die Beschreibtmg von Dis k ret i s i run e g s ve r fa h r en (B), die endlich- dimension ale Gleichungen fUr Niihertmgen der Lbsung ergeben. D r anschlieEende zweite Teil der Numerik ist die n u mer i s c h e A n a 1 y (C) s der e betreffenden Verfahren. Insbesondere ist zu kliiren, ob tmd wie schnell die Niiherung gegen die exakte Lbsung konvergiert. Die Auflbstmg der endlichdimensionalen Gleichtmgen CD, E) ist 3 6 i. allg. kein einfaches Problem, da 10 bis 10 Unbekannte auftreten kennen. Die Dis- kussion dieses dritten numerischen Problemkreises ist hier ausgespart (man findet es z. B.","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52433651106065,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52433651663121,"sku":"NLS9783658153571","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783658153571.jpg?v=1759178644"},{"product_id":"multi-grid-methods-and-applications-book-wolfgang-hackbusch-9783642057229","title":"Multi-Grid Methods and Applications","description":"Multi-grid methods are the most efficient tools for solving elliptic boundary value problems. One section describes special applications (convection-diffusion equations, singular perturbation problems, eigenvalue problems, etc.).","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52481033928977,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52481035141393,"sku":"NLS9783642057229","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783642057229.jpg?v=1789474035"},{"product_id":"elliptic-differential-equations-book-wolfgang-hackbusch-9783662572177","title":"Elliptic Differential Equations","description":"This book offers a simultaneous treatment of the theory and the numerical treatment of elliptic problems. The subjects dealt with include the classical theory (Green's function, maximum principle, etc.) as well as the variational formulation. The author describes and analyses finite difference and finite element methods. Specific chapters are devoted to the eigenvalue problem and the Stokes problem.","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52484713513233,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52484714463505,"sku":"NLS9783662572177","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783662572177.jpg?v=1786087898"},{"product_id":"tensor-spaces-and-numerical-tensor-calculus-book-wolfgang-hackbusch-9783030355562","title":"Tensor Spaces and Numerical Tensor Calculus","description":"Special numerical techniques are already needed to deal with n x n matrices for large n. Tensor data are of size n x n x...x n=nd, where nd exceeds the computer memory by far. Since standard methods fail, a particular tensor calculus is needed to treat such problems.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52489353920785,"sku":"NLS9783030355562","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":52760393744657,"sku":"NIN9783030355562","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783030355562.jpg?v=1786001395"},{"product_id":"tensor-spaces-and-numerical-tensor-calculus-book-wolfgang-hackbusch-9783030355531","title":"Tensor Spaces and Numerical Tensor Calculus","description":"Special numerical techniques are already needed to deal with n  n matrices for large n. Tensor data are of size n  n ... n=nd, where nd exceeds the computer memory by far. Since standard methods fail, a particular tensor calculus is needed to treat such problems.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52532756250897,"sku":"NLS9783030355531","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783030355531.jpg?v=1760662135"},{"product_id":"iterative-solution-of-large-sparse-systems-of-equations-book-wolfgang-hackbusch-9783319803609","title":"Iterative Solution of Large Sparse Systems of Equations","description":"C. F. GauS in a letter from Dec. 26, 1823 to Gerling: 3c empfe le 3 nen biegen IDlobu9 aur 9tac a mung. ec werlic werben eie ie wieber bi reet eliminiren, wenigftens nic t, wenn eie me r als 2 Unbefannte aben.: Da9 inbirecte 93erfa ren 109st sic alb im ec lafe ausfii ren, ober man fann wo renb be9gelben an anbere: Dinge benfen.  CO F. GauS: Werke vol. 9, Gottingen, p. 280, 1903] What difference exists between solving large and small systems of equations? The standard methods well-known to any student oflinear algebra are appli cable to all systems, whether large or small. The necessary amount of work, however, increases dramatically with the size, so one has to search for algo rithms that most efficiently and accurately solve systems of 1000, 10,000, or even one million equations. The choice of algorithms depends on the special properties the matrices in practice have. An important class of large systems arises from the discretisation of partial differential equations. In this case, the matrices are sparse (i. e., they contain mostly zeros) and well-suited to iterative algorithms. Because of the background in partial differential equa tions, this book is closely connected with the author's Theory and Numerical Treatment of Elliptic Differential Equations, whose English translation has also been published by Springer-Verlag. This book grew out of a series of lectures given by the author at the Christian-Albrecht University of Kiel to students of mathematics.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52532763984145,"sku":"NLS9783319803609","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783319803609.jpg?v=1760662172"},{"product_id":"concept-of-stability-in-numerical-mathematics-book-wolfgang-hackbusch-9783662513712","title":"The Concept of Stability in Numerical Mathematics","description":"\u003cp\u003eIn this book, the author compares the meaning of stability in different subfields of numerical mathematics.\u003c\/p\u003e\u003cp\u003eConcept of Stability in numerical mathematics opens by examining the stability of finite algorithms. A more precise definition of stability holds for quadrature and interpolation methods, which the following chapters focus on. The discussion then progresses to the numerical treatment of ordinary differential equations (ODEs). While one-step methods for ODEs are always stable, this is not the case for hyperbolic or parabolic differential equations, which are investigated next. The final chapters discuss stability for discretisations of elliptic differential equations and integral equations.\u003c\/p\u003e\u003cp\u003eIn comparison among the subfields we discuss the practical importance of stability and the possible conflict between higher consistency order and stability.\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52542126817553,"sku":"NLS9783662513712","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783662513712.jpg?v=1785771100"},{"product_id":"hierarchical-matrices-algorithms-and-analysis-book-wolfgang-hackbusch-9783662473238","title":"Hierarchical Matrices: Algorithms and Analysis","description":"However, the technique of hierarchical matrices makes it possible to store matrices and to perform matrix operations approximately with almost linear cost and a controllable degree of approximation error.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52589182320913,"sku":"NLS9783662473238","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783662473238.jpg?v=1786063237"},{"product_id":"iterative-solution-of-large-sparse-systems-of-equations-book-wolfgang-hackbusch-9783319284811","title":"Iterative Solution of Large Sparse Systems of Equations","description":"C. F. GauS in a letter from Dec. 26, 1823 to Gerling: 3c empfe le 3 nen biegen IDlobu9 aur 9tac a mung. ec werlic werben eie ie wieber bi reet eliminiren, wenigftens nic t, wenn eie me r als 2 Unbefannte aben.: Da9 inbirecte 93erfa ren 109st sic alb im ec lafe ausfii ren, ober man fann wo renb be9gelben an anbere: Dinge benfen.  CO F. GauS: Werke vol. 9, Gottingen, p. 280, 1903] What difference exists between solving large and small systems of equations? The standard methods well-known to any student oflinear algebra are appli cable to all systems, whether large or small. The necessary amount of work, however, increases dramatically with the size, so one has to search for algo rithms that most efficiently and accurately solve systems of 1000, 10,000, or even one million equations. The choice of algorithms depends on the special properties the matrices in practice have. An important class of large systems arises from the discretisation of partial differential equations. In this case, the matrices are sparse (i. e., they contain mostly zeros) and well-suited to iterative algorithms. Because of the background in partial differential equa tions, this book is closely connected with the author's Theory and Numerical Treatment of Elliptic Differential Equations, whose English translation has also been published by Springer-Verlag. This book grew out of a series of lectures given by the author at the Christian-Albrecht University of Kiel to students of mathematics.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52596912783633,"sku":"NLS9783319284811","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783319284811.jpg?v=1786094656"},{"product_id":"integral-equations-book-wolfgang-hackbusch-9783034899475","title":"Integral Equations","description":"The theory of integral equations has been an active research field for many years and is based on analysis, function theory, and functional analysis. On the other hand, integral equations are of practical interest because of the boundary integral equation method, which transforms partial differential equations on a domain into integral equations over its boundary. This book grew out of a series of lectures given by the author at the Ruhr-Universitat Bochum and the Christian-Albrecht-Universitat zu Kiel to students of mathematics. The contents of the first six chapters correspond to an intensive lecture course of four hours per week for a semester. Readers of the book require background from analysis and the foundations of numeri- cal mathematics. Knowledge of functional analysis is helpful, but to begin with some basic facts about Banach and Hilbert spaces are sufficient. The theoretical part of this book is reduced to a minimum; in Chapters 2, 4, and 5 more importance is attached to the numerical treatment of the integral equations than to their theory. Important parts of functional analysis (e. g., the Riesz-Schauder theory) are presented without proof. We expect the reader either to be already familiar with functional analysis or to become motivated by the practical examples given here to read a book about this topic. We recall that also from a historical point of view, functional analysis was initially stimulated by the investigation of integral equations.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52618039558417,"sku":"NLS9783034899475","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783034899475.jpg?v=1761532041"},{"product_id":"hierarchische-matrizen-book-wolfgang-hackbusch-9783642002212","title":"Hierarchische Matrizen","description":"\u003cp\u003eBei der Diskretisierung von Randwertaufgaben und Integralgleichungen entstehen große, eventuell auch voll besetzte Matrizen. Es wird eine neuartige Methode dargestellt, die es erstmals erlaubt, derartige Matrizen nicht nur effizient zu speichern, sondern auch alle Matrixoperationen einschließlich der Matrixinversion bzw. der Dreieckszerlegung approximative durchzuführen. \u003c\/p\u003e\n\u003cp\u003eAnwendungen findet diese Technik nicht nur bei der Lösung großer Gleichungssysteme, sondern auch bei Matrixgleichungen und der Berechnung von Matrixfunktionen.\u003c\/p\u003e","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52618325491985,"sku":"NLS9783642002212","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783642002212.jpg?v=1786354144"},{"product_id":"iterative-solution-of-large-sparse-systems-of-equations-book-wolfgang-hackbusch-9781461287247","title":"Iterative Solution of Large Sparse Systems of Equations","description":"C. F. GauS in a letter from Dec. 26, 1823 to Gerling: 3c empfe le 3 nen biegen IDlobu9 aur 9tac a mung. ec werlic werben eie ie wieber bi reet eliminiren, wenigftens nic t, wenn eie me r als 2 Unbefannte aben.: Da9 inbirecte 93erfa ren 109st sic alb im ec lafe ausfii ren, ober man fann wo renb be9gelben an anbere: Dinge benfen.  CO F. GauS: Werke vol. 9, Gottingen, p. 280, 1903] What difference exists between solving large and small systems of equations? The standard methods well-known to any student oflinear algebra are appli cable to all systems, whether large or small. The necessary amount of work, however, increases dramatically with the size, so one has to search for algo rithms that most efficiently and accurately solve systems of 1000, 10,000, or even one million equations. The choice of algorithms depends on the special properties the matrices in practice have. An important class of large systems arises from the discretisation of partial differential equations. In this case, the matrices are sparse (i. e., they contain mostly zeros) and well-suited to iterative algorithms. Because of the background in partial differential equa tions, this book is closely connected with the author's Theory and Numerical Treatment of Elliptic Differential Equations, whose English translation has also been published by Springer-Verlag. This book grew out of a series of lectures given by the author at the Christian-Albrecht University of Kiel to students of mathematics.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52622621770001,"sku":"NLS9781461287247","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9781461287247.jpg?v=1790189674"},{"product_id":"hierarchical-matrices-algorithms-and-analysis-book-wolfgang-hackbusch-9783662568941","title":"Hierarchical Matrices: Algorithms and Analysis","description":"\u003cp\u003eThis self-contained monograph presents matrix algorithms and their analysis. The new technique enables not only the solution of linear systems but also the approximation of matrix functions, e.g., the matrix exponential. Other applications include the solution of matrix equations, e.g., the Lyapunov or Riccati equation. The required mathematical background can be found in the appendix.\u003c\/p\u003e\u003cp\u003eThe numerical treatment of fully populated large-scale matrices is usually rather costly. However, the technique of hierarchical matrices makes it possible to store matrices and to perform matrix operations approximately with almost linear cost and a controllable degree of approximation error. For important classes of matrices, the computational cost increases only logarithmically with the approximation error. The operations provided include the matrix inversion and LU decomposition.\u003c\/p\u003e\u003cp\u003eSince large-scale linear algebra problems are standard in scientific computing, the subject of hierarchicalmatrices is of interest to scientists in computational mathematics, physics, chemistry and engineering.\u003c\/p\u003e","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52622656373009,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52622657028369,"sku":"NLS9783662568941","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783662568941.jpg?v=1785916102"},{"product_id":"boundary-elements-implementation-and-analysis-of-advanced-algorithms-book-wolfgang-hackbusch-9783322899439","title":"Boundary Elements: Implementation and Analysis of Advanced Algorithms","description":"The GAM Committee for Efficient Numerical Methods for Partial Differential Equations organizes seminars and workshops on subjects concerning the algorithmic treatment of partial differential equations. The topics are discretisation methods like the finite element and the boundary element method for various type of applications in struc- tural and fluid mechanics. Particular attention is devoted to advanced solution method. The latest seminar in this series was the 12th Kiel-Seminar which took place on January 19-21, 1996 at Christian-Albrechts-University of Kiel and focussed on the topic Boundary Elements: Implementation and Analysis of Advanced Algorithms. The seminar was attended by 65 scientists from 10 countries. 23 lectures were given, including two survey lectures. In the last years, a remarkable progress in the numerical treatment of boundary de- ment methods (BEM) has been obtained in Germany. This is, in particular, a res I1t of a Schwerpunktverfahren supported by the DFG. Many aspects of the BEM are not ouly analysed but also implemented. Therefore, these proceedings present a number of papers on implementational aspects besides the analysis of advanced techniques.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52627136971025,"sku":"NLS9783322899439","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783322899439.jpg?v=1761692713"},{"product_id":"numerical-treatment-of-coupled-systems-book-wolfgang-hackbusch-9783322868619","title":"Numerical Treatment of Coupled Systems","description":"The GAM Committee for Efficient Numerical Methods for Partial Differential Equations organizes seminars and workshops on subjects concerning the algorithmic treatment of partial differential equations. The topics are discretisation methods like the finite element and the boundary element method for various type of applications in structural and fluid mechanics. Particular attention is devoted to the advanced solution methods. The series of such seminars was continued in 1995, January 20-22, with the 11th Kiel-Seminar on the special topic Numerical Treatment of Coupled Systems at the Christian-Albrechts-University of Kiel. The seminar was attended by 100 scientist from 9 countries. 23 lectures were given, including two survey lectures. Different kinds of couplings are considered in this volume. The coupling of different components may occur in the physical model. On the other hand, a coupling of subsystems can be generated by the numerical solution technique. General examples of the latter kind are the domain decomposition (see p. 128) or subspace decomposition (p. 117). The local defect correction method couples different discretizations of the same problem in order to improve the results, although the basic linear system to be solved remains unchanged (p. 47). In general, the aim of the numerical coupling is to make use of (efficient) subsystem solvers (p. 1). The combination of different discretization techniques is mentioned on page 59.","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52627275448593,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52627275841809,"sku":"NLS9783322868619","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783322868619.jpg?v=1785917225"},{"product_id":"efficient-solutions-of-elliptic-systems-book-wolfgang-hackbusch-9783528080846","title":"Efficient Solutions of Elliptic Systems","description":null,"brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52662910615825,"sku":"NLS9783528080846","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783528080846.jpg?v=1762270659"},{"product_id":"theorie-und-numerik-elliptischer-differentialgleichungen-book-wolfgang-hackbusch-9783519020745","title":"Theorie und Numerik elliptischer Differentialgleichungen","description":"Dieses Buch ist aus Vorlestmgen entstanden, die der Autor an der Ruhr-Universitiit Bochum und an der Christian-Albrechts-Universitiit Kiel fUr Studenten der Mathematik gehalten hat. Die vorliegende Abhandltmg beschriinkt sich auf partielle Differentialgleichtmgen yom ell i p tis c hen Typ, da andemfalls die Darstelltmg entweder zu oberfliichlich oder zu umfangreich geriete. Die folgende Skizze zeigt, welche Aufgaben sich bei elliptischen Differentialgleichungen ergeben. A: Theorie der B: Diskretisierungen C: Numerische Analyse: elliptischen (Differenzenverfahren, Konvergenz, Gleichtmgen finite Elemente, etc) Stabilitiit elliptische diskrete Gleichung ---------------- Randwertaufgabe i D: Gleichungsauflbsung E: Theorie der a) direkt oder durch Iterationsverfahren b) I terationsverfahren Die The 0 r i e der elliptischen Gleichtmgen (A) beschiiftigt sich mit den Fragen nach Existenz, Eindeutigkeit und Eigenschaften der Lbsung. Das erste Problem der Numerik ist die Beschreibtmg von Dis k ret i s i run e g s ve r fa h r en (B), die endlich- dimension ale Gleichungen fUr Niihertmgen der Lbsung ergeben. D r anschlieEende zweite Teil der Numerik ist die n u mer i s c h e A n a 1 y (C) s der e betreffenden Verfahren. Insbesondere ist zu kliiren, ob tmd wie schnell die Niiherung gegen die exakte Lbsung konvergiert. Die Auflbstmg der endlichdimensionalen Gleichtmgen CD, E) ist 3 6 i. allg. kein einfaches Problem, da 10 bis 10 Unbekannte auftreten kennen. Die Dis- kussion dieses dritten numerischen Problemkreises ist hier ausgespart (man findet es z. B.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52664057266449,"sku":"NLS9783519020745","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783519020745.jpg?v=1785955394"},{"product_id":"multigrid-methods-v-book-wolfgang-hackbusch-9783540631330","title":"Multigrid Methods V","description":"This volume contains a selection from the papers presented at the Fifth European Multigrid Conference, held in Stuttgart, October 1-4, 1996. There were 88 registered participants from 14 different countries worldwide, and 65 lectures were given. Earlier European Multigrid Conferences were held in Cologne in 1981 and 1985, in Bonn in 1990, and in Amsterdam in 1993. The next European Conference is planned in 1999 in Gent. The European Multigrid Conference '96 was organized by the Institut fUr Computer- anwendungen (ICA) of Stuttgart University, in cooperation with the GAM Com- mittee for Scientific Computing, SFB 359 and 404 and the research network WiR Ba- Wii. The list of topics contained lectures on Multigrid Methods: robustness, adaptivity, wavelets, parallelization, application in computational fluid dynamics, porous media flow, optimisation and computational mechanics. A considerable part of the talks fo- cused on algebraic multigrid methods. The remaining contributions will be published by the Institut fUr Computeranwen- dungen (ICA) in Stuttgart in a special ICA report. Special thanks are due to Oktavia Klassen, who carefully compiled the contributions to this volume.","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52664196202769,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52664197087505,"sku":"NLS9783540631330","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783540631330.jpg?v=1785928833"},{"product_id":"concept-of-stability-in-numerical-mathematics-book-wolfgang-hackbusch-9783642393853","title":"The Concept of Stability in Numerical Mathematics","description":"In this book, the author compares the meaning of stability in different subfields of numerical mathematics.  Concept of Stability in numerical mathematics opens by examining the stability of finite algorithms. A more precise definition of stability holds for quadrature and interpolation methods, which the following chapters focus on. The discussion then progresses to the numerical treatment of ordinary differential equations (ODEs). While one-step methods for ODEs are always stable, this is not the case for hyperbolic or parabolic differential equations, which are investigated next. The final chapters discuss stability for discretisations of elliptic differential equations and integral equations.  In comparison among the subfields we discuss the practical importance of stability and the possible conflict between higher consistency order and stability.","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52667695366417,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52667695890705,"sku":"NLS9783642393853","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783642393853.jpg?v=1786700532"},{"product_id":"tensor-spaces-and-numerical-tensor-calculus-book-wolfgang-hackbusch-9783642280269","title":"Tensor Spaces and Numerical Tensor Calculus","description":"Special numerical techniques are already needed to deal with nxn matrices for large n.Tensor data are of size nxnx...xn=n^d, where n^d exceeds the computer memory by far. 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