Trefftz and collocation methods

• Main Authors: Li, Z.-C, Lu, T.-T, Hu, H.-Y, Cheng, A. H.-D
• Format: eBook
• Language: English
• Published: Southampton WIT Press 2008; WIT
• Edition: 1
• Subjects: Boundary element methods; Collocation methods; Meshfree methods (Numerical analysis)

This book covers a class of numerical methods that are generally referred to as “Collocation methods”. Different from the Finite Element and the Finite Difference methods, the discretization and approximation of the collocation method is based on a set of unstructured points in space. This “meshless...

Table of Contents:

• Trefftz and collocation methods -- Contents -- Preface -- Acknowledgements -- Tutorial introduction -- Part I: Collocation Trefftz method -- 1. Basic algorithms and theory -- 2. Motz's problem and its variants -- 3. Coupling techniques -- 4. Biharmonic equations with singularities -- Part II: Collocation methods -- 5. Collocation methods -- 6. Combinations of collocation and finite element methods -- 7. Radial basis function collocation methods -- Part III: Advanced topics -- 8. Combinations with high-order FEMs -- 9. Eigenvalue problems -- 10. The Helmholtz equation -- 11. Explicit harmonic solutions of Laplace’s equation -- Appendix: Historic review of boundary methods -- References -- Glossary of symbols -- Index.
• Cover -- Trefftz and Collocation Methods -- Copyright page -- Contents -- The bust image of Erich Trefftz (1888&amp -- #8211 -- 1937) -- Preface -- Acknowledgements -- Tutorial introduction -- I.1 Algorithms of CM, TM, and CTM -- I.2 Coupling techniques -- I.3 Boundary element methods -- I.4 Other kinds of boundary methods -- I.5 Comparisons -- Part I: Collocation Trefftz method -- 1. Basic algorithms and theory -- 2. Motz's problem and its variants -- 3. Coupling techniques -- 4. Biharmonic equations with singularities -- Part II: Collocation methods -- 5. Collocation methods -- 6. Combinations of collocation and finite element methods -- 7. Radial basis function collocation methods -- Part III: Advanced topics -- 8. Combinations with high-order FEMs -- 9. Eigenvalue problems -- 10. The Helmholtz equation -- 11. Explicit harmonic solutions of Laplace's equation -- Appendix Historic review of boundary methods -- A.1 Potential theory -- A.2 Existence and uniqueness -- A.3 Reduction in dimensions and Green's formula -- A.4 Integral equations -- A.5 Extended Green's formula -- A.6 Pre-electronic computer era -- A.7 Electronic computer era -- A.8 Boundary integral equation and boundary element methods -- References -- Glossary of symbols -- Index -- A -- B -- C -- D -- E -- F -- G -- H -- I -- J -- L -- M -- N -- O -- P -- Q -- R -- S -- T -- U -- V -- W -- Z