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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 approachАвтор: 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.
Язык: Рубрика: Computer science /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 2006Количество страниц: 524Добавлена в каталог: 29.10.2010Операции: Положить на полку |
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Member, public, in inheritance 81 82 Memory 3 370 Memory, allocation 5 33 68 Memory, allocation, in dynamic vector 95 Memory, distributed 374 Memory, in array 23 Memory, in constructor 51 54 Memory, in destructor 55 Memory, in recursion 26 Memory, in template 74 Memory, long 150 173 207 Memory, primary 3 371 Memory, secondary 3 371 Memory, shared 373 Memory, short 150 158 168 207 Merging connected lists 108 mesh 133 Mesh, implementation of 291 Mesh, in ODE 163 166 Mesh, nonuniform 259 281 297 Mesh, refinement 304 Mesh, uniform 266 Mesh, unstructured 259 281 Meshsize, in ODE 163 166 Meshsize, in PDE 188 Meshsize, in PDE, in two dimensions 205 Midpoint scheme 193 see MIMD 374 Minimization problem 252 Minimization problem, in elasticity 405 Model, circular 432 Model, physical 194 Model, rectangular 431 Modular 5 Molecule 365 Multigrid 351 355 362 398 466 Multigrid, algebraic 354 362 398 469 Multigrid, black-Box 364 Multigrid, in elasticity 408 Multigrid, nonsymmetric 362 Multilevel programming 136 nabla 413 Navier — Stokes equations 423 Negative definite 421 NEW 95 see Newton — Rabson 229 Newton, binomial 30 152 Newton, iteration, in denoising 240 241 Newton, iteration, in Navier — Stokes 423 Newton, iteration, in Riemann 229 230 Newton, iteration, in system 234 Node 133 Node, array of 124 Node, implementation of 284 Node, in graph 114 122 Node, in triangulation 128 Nonlinear PDE 219 see Nonsymmetric system 353 362 Nonuniform mesh 297 see Normal equation 346 378 465 Numerical, approximation 209 Numerical, approximation, in Helmholtz 427 Numerical, approximation, in ODE 165 171 Numerical, approximation, in PDE 185 262 302 341 Numerical, approximation, in Stokes 421 Numerical, example, in denoising 242 Numerical, example, in elasticity 409 Numerical, scheme 133 see “Implicit “Semi-implicit Numerical, solution, in ODE 165 176 Numerical, solution, in PDE 396 Numerical, solution, of linear system 323 Object 5 47 198 Object, abstract 281 Object, concrete 281 see Object, current 49 54 Object, current, "const" 63 Object, current, "this" 56 59 64 Object, current, in inheritance 81 139 Object, current, in template 75 Object, current, nonconstant 65 70 Object, current, reference to 62 Object, current, temporary 67 Object, local 137 see Object, returned 54 65 144 Object, returned, constructed 137 Object, returned, nonreference 70 71 Object, returned, temporary 54 Object, returned, type of 60 Object, temporary 67 140 Object, temporary, nonconstant 65 Object, temporary, pointer to 54 Object, temporary, returned 68 Object, temporary, to change 61 64 140 Object-oriented 282 Object-oriented, analysis 170 Object-oriented, implementation 135 Object-oriented, language 5 47 121 Object-oriented, programming 65 68 121 ODE 161 ODE, nonlinear 170 ODE, stable 162 ODE, system of 162 ODE, system of, stable 163 Open a file 25 Operation 9 see Operator 62 Operator, arithmetic 68 see Operator, assignment 60 Operator, assignment, of complex 69 Operator, assignment, of connected list 105 Operator, assignment, of dynamic vector 97 Operator, assignment, of list 101 Operator, binary 65 Operator, curl 415 Operator, differential 417 423 Operator, divergence 414 see Operator, gradient 413 497 see Operator, Laplacian 414 Operator, logical 14 see Operator, nabla 413 Operator, rotor 415 Operator, unary 63 Ordering connected list 110 Output 13 pade 42 90 Parallel, architecture 373 Parallel, computer 369 Parallel, implementation 369 383 475 Parallelism 369 381 Parallelizable 370 381 Pascal, calculation machine 3 Pascal, triangle 29 152 PCG 359 see PDE xxiii PDE, elliptic 182 PDE, hyperbolic 183 PDE, nonlinear 219 PDE, nonlinear, indenoising 238 PDE, nonlinear, system 423 PDE, nonlinear, system of 233 241 PDE, parabolic 183 PDE, system of 233 403 416 434 PDE, three-dimensional 436 PDE, time-dependent 400 PDE, two-dimensional 205 417 444 Picard 229 POINTER 22 Pointer, as argument 25 Pointer, in connected list 102 Pointer, to "point" object is returned 56 Pointer, to character 23 24 Pointer, to connected list converted from 303 304 306 330 332 Pointer, to constant 23 56 290 Pointer, to constant point 56 Pointer, to double 22 24 95 Pointer, to file 25 386 Pointer, to integer 22 25 Pointer, to mesh 303 Pointer, to mesh, converted to 294 303 304 306 Pointer, to mesh, local 461 Pointer, to multigrid 355 Pointer, to node in triangle 283 286 Pointer, to nonconstant 23 290 Pointer, to point 56 Pointer, to pointers 24 Pointer, to row converted to 330—332 Pointer, to static file 40 Pointer, to T 99 Pointer, to temporary object 55 Poisson, equation 182 Poisson, equation, in a circle 274 476 Poisson, equation, in FOSLS 423 Poisson, equation, Jacobi iteration for 345 Poisson, equation, one-dimensional 276 Poisson, equation, stiffness matrix in 294 Poisson, ratio 403 409 411 Poisson, ratio, in Stokes 420 Polynomial 138 Polynomial, calculation of 143 144 Polynomial, integration of 154 Polynomial, multiplication of 141 Polynomial, of three variables 159 Polynomial, of two variables 152 400 Polynomial, of two variables, cubic 316 Polynomial, of two variables, quadratic 314 Polynomial, time 3 4 Positive definite 262 Preconditioner 343 361 383 395 Preconditioner, in elasticity 403 Preconditioner, in Stokes 419 primary memory 3 371 see print 13 see “"fprintf"” PRIVATE 49 see private member 56 see Problem, boundary value 251 Problem, computational 3 135 369 380 Problem, initial-boundary value 187 Problem, measuring 430 Problem, minimization 252 Problem, minimization, in elasticity 405 Process 121 Processor 3 370 Processor, main 375 Processors 369 373 PROGRAM 3 Program, executable 375 Programming 3 Prolongation 352 354 362 468 protected 81 see protected member 81 see PUBLIC 49 see public member 67 see Quadratic 314 see Quadratic form 253 255 261 Quadratic form, in elasticity 405 Quadratic form, in FOSLS 423 Random-choice scheme 225 Rarefaction wave 220 231 READ 25 see Rectangular, domain 205 238 266 Rectangular, grid 190 Rectangular, matrix 352 Recursion 26 Recursion, in arithmetic expression 36 Recursion, in binary representation 27 Recursion, in connected list 107 Recursion, in local maximum 35 Recursion, in mesh refinement 304 Recursion, in multigrid 355 Recursion, in row 331 Reference 57 Reference element 428 Reference triangle, cubic 316 Reference triangle, linear 263 314 Reference triangle, quadratic 314 Reference, to pass a reference, to finite element 291 Reference, to pass a reference, to node 302 Reference, to pass a reference, to row 465 Reference, to pass a reference, to vector 332 345 470 Reference, to return a 59 66 70 350 referencing 121 refinement 304 Refinement, adaptive 299 476 Refinement, adaptive, in elasticity 408 Refinement, boundary 297 307 Refinement, global 297 312 396 400 Refinement, local 297 Regularity 305 Relaxation 371 see “Gauss Reserved word 4 RETURN 12 33 Return, by reference 59 66 70 350 466 Return, by value 59 66 70 350 465 466 Returned 54 see “"const"” Returned object 54 “Object” Reynolds number 423 Riemann problem 219 Riemann problem, linearized 230 Riemann problem, N-wave 226 Riemann problem, singularly perturbed 226 228 230 233 Rotor 415 Row object 329 Run 4 Run, time 4 24 26 Run, time, in connected list 105 Run, time, in dynamic vector 95 Run, time, in list 99 SCAN 25 see Scheme 133 see “Implicit “Semi-implicit Schur complement 421 422 Schur complement, in PDEs 417 Schwarz iteration 373 Scope 15 Secondary memory 3 371 Semi-implicit scheme 193 212 399 Sequential, algorithm 370 Sequential, computer 369 SHAPE 128 Shared memory 373 Shockwave 221 231 SIMD 17 Singular perturbation 226 Solution, asymptotic 174 Solution, irregular 423 Solution, numerical 165 see Solution, unique 255 Sparse matrix 124 see Sparsity 318 SPD 262 360 383 Stability 209 212 456 Stable ODE 162 see Standard I/O 13 see State machine 12 51 121 Static file 40 Stiffness matrix 259 see Stiffness system 260 Stokes equations 418 419 Storage 51 137 Storage, in inheritance 82 String 24 36
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