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Shapira Y. — Solving PDEs in C++: numerical methods in a unified object-oriented approach
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Название: Solving PDEs in C++: numerical methods in a unified object-oriented approach
Автор: Shapira Y.
Аннотация: This book teaches C++ and uses it to solve partial differential equations (PDEs). Basic and advanced numerical methods are introduced and implemented easily and efficiently in a unified object-oriented approach.
The powerful features and advanced tools available in C++ are particularly useful for implementing the complex mathematical objects that are often used in numerical modeling. The code segments and their detailed explanations show how easy it is to implement advanced algorithms such as finite elements and multigrid.
The book contains such as six parts. The first two parts introduce C, C++, and the object-oriented approach. The third and fourth parts describe and implement finite-difference and finite-element schemes. The fifth part deals with numerical linear algebra and parallelism. The sixth and final part uses the present approach in advanced applications. Each chapter ends with exercises and solutions.
The book contains two theoretical chapters, which can be skipped by readers who are interested in only the practical aspects (Chapters 8 and 11 and also Sections 9.9, 12.7, 18.16, and 20.4-20.5). More advanced readers may find them most useful and relevant to the present methods.
Because the book already contains the required background in programming, PDEs, and numerical methods, the only prerequisites are calculus and linear algebra. It can thus be used as a textbook in courses on C++ for scientific computing, C++ for engineers, numerical analysis, and numerical PDEs in the advanced undergraduate and graduate levels. Because it is self-contained, it is also suitable for self-study by researchers and students in applied and computational sciences and engineering.
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Рубрика: Computer science /
Статус предметного указателя: Готов указатель с номерами страниц
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Год издания: 2006
Количество страниц: 524
Добавлена в каталог: 29.10.2010
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Предметный указатель
"!=" 14
"%c" 20 37
"%d" 13
"%f" 13
"&&" 14
"()" 11 13
"(double)" 9
"(float)" 43
"(hit)" 9
"*/" 8
"*=" 10
"*=", in complex 82
"*=", in sparse matrix 462
"+ =" 10
"+ =", in complex 69
"+ =", in dynamic vector 443
"+ =", in matrix 441
"+ =", in point 64
"+ =", in sparse matrix 462
"++" 10
"- =" 10
"- =", in dynamic vector 442
"- =", in sparse matrix 462
"- =", in vector 439
"- >" 56
"--" 10
"/*" 8
"//" 8
"/=" 10
"/=", in complex 82
": :" 50
":public" 80
"<=" 14
"==" 14
">=" 14
"? :" 14
"char" 7 39
"const" 9
"const", argument 61
"const", current object 50 56 63
"const", current object, in template 74
"const", returned variable 54 56 466
"delete []" 96
"delete" 55
"delete", in template 73 287
"do" 18
"double" 7
"else" 15
"FILE" 25 386
"float" 7
"fopen" 25 386
"for" 18
"fprintf' 25
"fscanf" 25 386
"getchar" 39
"if" 14 15
"include" 13 20
"int" 7 11
"main" 13
"math.h" 17
"new" 134 287 342
"new", connected list 104
"new", dynamic vector 95
"new", graph 115
"new", row 349 379
"printf 13
"private" 49
"private:" 50
"protected" in connected list 103
"protected" in dynamic vector 95 446
"protected" in list 199 201 386 453
"protected" in polynomial 139
"protected:" 81
"public:" 49 68 73
"return" 12
"scanf" 25
"sizeof" 43
"static" 40
"stdio.h" 13
"this" 56 59
"typedef", cubic triangle 317
"typedef", matrix 87 441
"typedef", point 78
"typedef", quadratic triangle 315
"typedef", triangle 290
"void" 11 12
"while" 17 18
"[]" 23
"| |" 15
'!' 14
'%' 9 38 146
'&' 58 121
'*' 22 121
'.' 49
':' 52 80
';' 6
'<' 14
'=' 8 14
'>' 14
'~' 55
Accuracy 214
Adaptive, discretization 194
Adaptive, mesh see “Refinement” 194
Adaptive, refinement see “Refinement” 299
Address 22
Address, of nodes 283
Address, to pass an 25 26 54 57
Address, to pass an, to temporary object 55
Address, virtual 121
Address, virtual, in Harwell-Boeing 385
Address, virtual, of nodes 125 129
Address, virtual, of nonzeroes 385
Adequacy 214 272
Adequacy, in Helmholtz 427 429
Adequacy, in Riemann 230
Adequacy, in Stokes 419
ADI 234
Algorithm 3 136 143
Algorithm, inherently sequential 370
Algorithm, parallelizable 370
ALLOCATE 5 51
Alternating, direction 234
Alternating, Schwarz relaxation 373
AMG 354 see
AMGe 365
AMGM 365
Anisotropic 249 271
Anisotropic, in Stokes 419
Architecture 370 380
Architecture, parallel 373 385
Architecture, sequential 385
Argument, by address 25 54
Argument, by name 24 57 470
Argument, by reference 59 73
Argument, by value 24 54 57 59 73
Argument, concrete 12 16
Argument, concrete, constant 61
Argument, concrete, in template 75
Argument, concrete, local copy 24 54
Argument, concrete, local reference 58
Argument, dummy 11 17 121
Argument, local 12 see
Argument, that is a pointer 25
Arithmetic, expression 36
Arithmetic, operation 9 196
Arithmetic, operation, on complex 68
Arithmetic, operation, on dynamic vector 98
Arithmetic, operation, on matrix 90
Arithmetic, operation, on polynomial 138
Arithmetic, operation, on sparse matrix 462
Arithmetic, operation, on vector 75
Arithmetic, operation, priority order of 9
Array 23 121
Array, of addresses 282
Array, of edges 125
Array, of nodes 124
Array, of same-size objects 111
Array, two-dimensional 24 29
assembling 265 293 337
Assembling, inelasticity 481
Assembling, quadratic 316
ASSIGNMENT 8
assignment operator 60 see
Automaton 12 51 121
Back substitution 89 347 465
base class 80 199 445
Bilinear form 251 261 295 399
Bilinear form, in Navier — Stokes 424
Binary representation 22 27 376
Bisection 30
Block, in a matrix 212
Block, of a function 11
Block, of class 71
Block, of instructions 4 15
Block, relaxation 373 385 388
Boundary, condition 190 250 478
Boundary, condition, Dirichlet (first kind) 181 190 481
Boundary, condition, in elasticity 481
Boundary, condition, mixed (third kind) 182 187 425 427
Boundary, condition, Neumann (second kind) 182
Boundary, curved 133 309
Boundary, irregular 133 298 397
Boundary, layer 184
Boundary, refinement 307 398
Boundary, refinement, in elasticity 411
Boundary, refinement, in Stokes 419
Boundary-value problem 251
Cache 371
Cache, oriented 371 373
CG 359 see
Chain rule 265
Chain rule, in Riemann 220 232
CHARACTER 7 see
Characteristic 220 228 232 234
class 48
Code 3
Coercivity 253
Coercivity, in elasticity 405
Column pointer 385
comment 8
Communication 375
Compilation, error 23
Compilation, error, constant 50
Compilation, error, due to ambiguity 85
Compilation, error, temporary 54 61
Compilation, time 4 5
Compilation, time, in array 23
Compilation, time, in recursion 26
Compilation, time, in template 72
Compiler 9
Compiler, in assignment 60 61
Compiler, in constructor 51 52 54
Compiler, in conversion 63
Compiler, in function 12 17
Compiler, in inheritance 81
Compiler, in operator 64 66 67
Compiler, in pointer 23
Compiler, in reference 58
Compiler, in template 72
Complex number 68
Complex number, implementation of 68
Complex number, implementation of, (has a) 79
Complex number, implementation of, (is a) 80
complexity 369 380
Complexity, in graph 123
Complexity, in triangulation 129 131
Computable problem 3
Computable problem, in polynomial time 4
Computational, problem 3 135 369 380
Computational, task 3 369
Computer 370
Computer, digital 3
Computer, parallel 369
Computer, sequential 369
Concrete object 281 see
Concrete variable 17 see
conformal 129 259
Conformity 259 273 301 302
Conjugate gradient 359
Conjugate gradient, preconditioned 359 470
Conjugate gradient, squared 361 472
Connected list 102 111
Connected list, flexibility of 112 132
Connected list, in row 329
Connected list, in sparse matrix 127 325
Connected list, in triangulation 131 133 291
Connected list, of edges 126
Connected list, of integers 127 282
Connected list, of nodes 282
Connected list, of triangles 132 284 291
Connected list, two-sided 112
Connection Machine 375
Conservation law 219 232
Conservation law, system of 234
Constant 9 see
constructor 51 287
Constructor, default 51
Constructor, default, in dynamic vector 446
Constructor, default, in inheritance 81 202
Constructor, default, in list 199 200 449
Constructor, default, in template 74
Constructor, in assembling 337
Constructor, in assembling, in elasticity 481
Constructor, in dynamic vector 95 446
Convection-diffusion 187 444
Conversion 9
Conversion, explicit 53
Conversion, explicit, of pointers 294 303 304 306 330—332
Conversion, implicit 53
Conversion, implicit, in inheritance 85
Conversion, inverse 63
copy constructor 59 71 287
Copy constructor, default 53 450
Copy constructor, default, in dynamic vector 446
Copy constructor, default, in template 74
Copy constructor, in connected list 103
Copy constructor, in dynamic vector 97 446
Copy constructor, in inheritance 450
Copy constructor, in list 101
Copy constructor, in template 74
Copy constructor, in vector 76
Crank — Nicolson 193 see
Cubic 316 see
Curl 415
current object 54 see
Data access, cache 371
Data access, edge-to-node 125
Data access, node-to-edge 126
Data access, node-to-triangle 131
Data access, primary memory 371
Data access, secondary memory 371
Data access, triangle-to-node 131 133
Data structure 93 121
Data structure, for mesh 247
Data structure, for sparse matrix 325
Data structure, to store triangles 131
Data structure, uses pointers 127
DEBUG 5
declaration 50 57 66 448
Degenerate triangle 262 276
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