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Shapira Y. — Solving PDEs in C++: numerical methods in a unified object-oriented approach
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.


Язык: en

Рубрика: Computer science/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2006

Количество страниц: 524

Добавлена в каталог: 29.10.2010

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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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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