Computational partial differential equations using Matlab:
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| Main Author: | |
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| Format: | Book |
| Language: | English |
| Published: |
London
CRC PRESS
2019
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| Edition: | 2. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 408 Seiten Illustrationen, Diagramme |
| ISBN: | 0367217740 9780367217747 |
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MARC
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| adam_text | Contents Preface xi Acknowledgments 1 Brief Overview of Partial Differential Equations 1.1 1.2 1.3 1.4 The parabolic equations ............................................................ The wave equations..................................................................... The elliptic equations ............................................................... Differential equations in broader areas .................................... 1.4.1 Electromagnetics............................................................ 1.4.2 Fluid mechanics............................................................... 1.4.3 Groundwater contamination.......................................... 1.4.4 Petroleum reservoir simulation .................................... 1.4.5 Finance modeling............................................................ 1.4.6 Image processing............................................................ 1.5 A quick review of numerical methods for PDEs ..................... References ............................................................................................. 2 Finite Difference Methods for ParabolicEquations 2.1 2.2 2.3 Introduction................................................................................. Theoretical issues: stability, consistence, and convergence . . 1-D parabolic equations ............................................................ 2.3.1 The 0-method and its analysis........................................ 2.3.2 Some extensions ............................................................ 2.4 2-D and 3-D parabolic equations
............................................. 2.4.1 Standard explicit and implicit methods......................... 2.4.2 The ADI methods for 2-D problems ............................ 2.4.3 The ADI methods for 3-D problems ............................ 2.5 Numerical examples with MATLAB codes .............................. 2.6 Bibliographical remarks ............................................................ 2.7 Exercises....................................................................................... References ............................................................................................. 3 Finite Difference Methods forHyperbolic Equations 3.1 3.2 3.3 Introduction................................................................................. Some basic difference schemes................................................... Dissipation and dispersion errors ............................................. xiii 1 1 2 3 3 3 4 5 6 7 8 9 H 13 13 16 18 18 23 27 27 30 32 35 37 38 41 43 43 44 47 v
vi Contents 3.4 3.5 Extensions to conservation laws................................................ The second-order hyperbolic equations .................................... 3.5.1 The 1-D case.................................................................. 3.5.2 The 2-D case.................................................................. 3.6 Numerical examples with MATLAB codes .............................. 3.7 Bibliographical remarks ............................................................ 3.8 Exercises....................................................................................... References ....................................................................................... 4 Finite DifferenceMethods forEllipticEquations 4.1 4.2 Introduction................................................................................ Numerical solution of linear systems ....................................... 4.2.1 Direct methods............................................................... 4.2.2 Simple iterative methods................................................ 4.2.3 Modern iterative methods............................................. 4.3 Error analysis with a maximum principle................................. 4.4 Some extensions ........................................................................ 4.4.1 Mixed boundary conditions.......................................... 4.4.2 Self-adjoint problems...................................................... 4.4.3 A fourth-order scheme................................................... 4.5 Numerical examples
with MATLAB codes .............................. 4.6 Bibliographical remarks ............................................................ 4.7 Exercises....................................................................................... References ....................................................................................... 5 High-OrderCompactDifference Methods 49 50 50 53 57 59 60 62 65 65 67 67 69 72 74 76 77 78 78 81 84 84 86 89 One-dimensional problems......................................................... 89 5.1.1 Spatial discretization...................................................... 89 5.1.2 Dispersive error analysis................................................ 94 5.1.3 Temporal discretization................................................ 98 5.1.4 Low-pass spatial filter.....................................................103 5.1.5 Numerical examples with MATLAB codes.................... 104 5.2 High-dimensional problems ........................................................121 5.2.1 Temporal discretization for 2-D problems.................... 121 5.2.2 Stability analysis..............................................................123 5.2.3 Extensions to 3-D compact ADI schemes....................... 124 5.2.4 Numerical examples with MATLAB codes.................... 125 5.3 Other high-order compact schemes ............................................ 133 5.3.1 One-dimensional problems............................................... 133 5.3.2 Two-dimensional problems............................................... 135 5.4 Bibliographical
remarks .............................................................. 138 5.5 Exercises.........................................................................................138 References ......................................................................................... 141 5.1 vii Contents 6 Finite Element Methods: Basic Theory 145 Introduction to one-dimensional problems ................................ 145 6.1.1 The second-order equation............................................... 145 6.1.2 The fourth-order equation............................................... 148 6.2 Introduction to two-dimensional problems ..............................152 6.2.1 The Poisson equation ..................................................... 152 6.2.2 The biharmonic problem.................................................. 154 6.3 Abstract finite element theory...................................................155 6.3.1 Existence and uniqueness.............................................156 6.3.2 Stability and convergence.............................................157 6.4 Examples of conforming finite element spaces .......................... 158 6.4.1 Triangular finite elements.............................................159 6.4.2 Rectangular finite elements..........................................163 6.5 Examples of nonconforming finite elements ............................. 164 6.5.1 Nonconforming triangular elements................................ 164 6.5.2 Nonconforming rectangular elements...........................165 6.6 Finite element interpolation
theory............................................ 167 6.6.1 Sobolev spaces................................................................. 167 6.6.2 Interpolation theory........................................................ 169 6.7 Finite element analysis of elliptic problems................................ 173 6.7.1 Analysis of conforming finite elements.......................... 173 6.7.2 Analysis of nonconforming finite elements.................... 175 6.8 Finite element analysis of time-dependent problems................. 177 6.8.1 Introduction....................................................................... 177 6.8.2 FEM for parabolic equations ......................................... 178 6.9 Bibliographical remarks .............................................................. 185 6.10 Exercises......................................................................................... 186 References ............................................................................................... 188 6.1 7 Finite Element Methods: Programming 193 7.1 FEM mesh generation ................................................................. 193 7.2 Forming FEM equations .............................................................. 198 7.3 Calculation of element matrices .................................................. 199 7.4 Assembly and implementation of boundary conditions .... 204 7.5 The MATLAB code for Pi element ............................................ 205 7.6 The MATLAB code for the Q element ................................... 208 7.7 Bibliographical
remarks .............................................................. 213 7.8 Exercises......................................................................................... 214 References ............................................................................................... 217 8 Mixed Finite Element Methods 8.1 8.2 219 An abstract formulation .............................................................. 219 Mixed methods for elliptic problems ......................................... 223 8.2.1 The mixed variational formulation................................ 223 8.2.2 The mixed finite element spaces...................................... 225 8.2.3 The error estimates........................................................... 229
viii Contents 8.3 Mixed methods for the Stokes problem....................................... 232 8.3.1 The mixed variational formulation................................. 232 8.3.2 Mixed finite element spaces..............................................234 8.4 An example MATLAB code for the Stokes problem..................238 8.5 Mixed methods for viscous incompressible flows........................ 252 8.5.1 The steady Navier-Stokes problem................................. 252 8.5.2 The unsteady Navier-Stokes problem.............................. 254 8.6 Bibliographical remarks ................................................................ 255 8.7 Exercises............................................................................................ 256 References ...................................................................................................259 9 Finite ElementMethods forElectromagnetics 261 9.1 Introduction to Maxwell’s equations ...........................................261 9.2 The time-domain finite difference method ................................. 263 9.2.1 The semi-discrete scheme..................................................263 9.2.2 The fully discrete scheme................................................. 272 9.3 The time-domain finite element method .................................... 285 9.3.1 The mixed method..............................................................285 9.3.2 The standard Galerkin method........................................ 290 9.3.3 The discontinuous Galerkin method .............................. 293 9.4 The
frequency-domain finite element method ........................... 298 9.4.1 The standard Galerkin method........................................298 9.4.2 The discontinuous Galerkin method .............................. 299 9.4.3 The mixed DG method .................................................... 303 9.5 Maxwell’s equations in dispersive media .................................... 305 9.5.1 Isotropic cold plasma.......................................................... 306 9.5.2 Debye medium................................................................... 310 9.5.3 Lorentz medium ................................................................ 313 9.5.4 Double-negative metamaterials........................................315 9.6 Bibliographical remarks ................................................................ 323 9.7 Exercises............................................................................................ 324 References .................................................................................................. 325 10 Meshless Methods withRadial Basis Functions 331 10.1 Introduction...................................................................................... 331 10.2 The radial basis functions ............................................................. 332 10.3 The MFS-DRM................................................................................ 335 10.3.1 The fundamental solution of PDEs................................. 335 10.3.2 The MFS for Laplace’s equation .................................... 338 10.3.3 The MFS-DRM for
elliptic equations.............................. 341 10.3.4 Computing particular solutions using RBFs..................344 10.3.5 The RBF-MFS................................................................... 346 10.3.6 The MFS-DRM for the parabolic equations..................346 10.4 Kansa’s method................................................................................ 348 10.4.1 Kansa’s method for elliptic problems............................. 348 Contents 10.4.2 Kansa’s method for parabolic equations........................ 349 10.4.3 The Hermite-Birkhoff collocation method..................... 350 10.5 Numerical examples with MATLAB codes ................................. 352 10.5.1 Elliptic problems................................................................ 352 10.5.2 Biharmonic problems.......................................................... 359 10.6 Coupling RBF meshless methods with DDM.............................. 366 10.6.1 Overlapping DDM............................................................. 367 10.6.2 Non-overlapping DDM....................................................... 368 10.6.3 One numerical example .................................................... 369 10.7 Bibliographical remarks ................................................................ 372 10.8 Exercises............................................................................................ 372 References ............................................................................................. 373 11 Other MeshlessMethods 379 11.1 Construction of meshless shape
functions.................................... 379 11.1.1 The smooth particle hydrodynamics method..................379 11.1.2 The moving least-square approximation........................ 381 11.1.3 The partition of unity method...........................................382 11.2 The element-free Galerkin method ..............................................384 11.3 The meshless local Petrov-Galerkin method .............................. 386 11.4 Bibliographical remarks ................................................................ 389 11.5 Exercises............................................................................................ 389 References ..............................................................................................390 Appendix A Answers toSelected Problems 393 Index 405
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| any_adam_object | 1 |
| author | Li, Jichun |
| author_facet | Li, Jichun |
| author_role | aut |
| author_sort | Li, Jichun |
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| building | Verbundindex |
| bvnumber | BV046219850 |
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| ctrlnum | (OCoLC)1135427512 (DE-599)BVBBV046219850 |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| isbn | 0367217740 9780367217747 |
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| spelling | Li, Jichun. Verfasser aut Computational partial differential equations using Matlab 2. ed. London CRC PRESS 2019 XIII, 408 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Differentialgleichung (DE-588)4012249-9 gnd rswk-swf Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf MATLAB (DE-588)4329066-8 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf Computermathematik (DE-588)4788218-9 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 s MATLAB (DE-588)4329066-8 s Computermathematik (DE-588)4788218-9 s DE-604 Partielle Differentialgleichung (DE-588)4044779-0 s Numerisches Verfahren (DE-588)4128130-5 s 1\p DE-604 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=031598539&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Li, Jichun Computational partial differential equations using Matlab Differentialgleichung (DE-588)4012249-9 gnd Numerisches Verfahren (DE-588)4128130-5 gnd MATLAB (DE-588)4329066-8 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd Computermathematik (DE-588)4788218-9 gnd |
| subject_GND | (DE-588)4012249-9 (DE-588)4128130-5 (DE-588)4329066-8 (DE-588)4044779-0 (DE-588)4788218-9 |
| title | Computational partial differential equations using Matlab |
| title_auth | Computational partial differential equations using Matlab |
| title_exact_search | Computational partial differential equations using Matlab |
| title_full | Computational partial differential equations using Matlab |
| title_fullStr | Computational partial differential equations using Matlab |
| title_full_unstemmed | Computational partial differential equations using Matlab |
| title_short | Computational partial differential equations using Matlab |
| title_sort | computational partial differential equations using matlab |
| topic | Differentialgleichung (DE-588)4012249-9 gnd Numerisches Verfahren (DE-588)4128130-5 gnd MATLAB (DE-588)4329066-8 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd Computermathematik (DE-588)4788218-9 gnd |
| topic_facet | Differentialgleichung Numerisches Verfahren MATLAB Partielle Differentialgleichung Computermathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=031598539&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT lijichun computationalpartialdifferentialequationsusingmatlab |