Availability: Stochastic methods for boundary value problems

Stochastic methods for boundary value problems: numerics for high-dimensional PDEs and applications

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Bibliographic Details
Main Authors:	Sabel'fel'd, Karl K. 1953- (Author), Simonov, Nikolai A. (Author)
Format:	Book
Language:	English
Published:	Berlin ; Boston De Gruyter [2016]
Subjects:	Irrfahrtsproblem Randwertproblem Monte-Carlo-Simulation Partielle Differentialgleichung Integralgleichung
Links:	http://www.degruyter.com/search?f_0=isbnissn&q_0=9783110479065&searchTitles=true http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029177302&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Physical Description:	ix, 198 Seiten 4 Diagramme 24 cm x 17 cm
ISBN:	3110479060 9783110479065 9783110479461

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Record in the Search Index

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adam_text	CONTENTS 1 2 2.1 2.2 2.3 2.4 2.5 3 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.7.1 3.8 3.9 4 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 INTRODUCTION * 1 RANDOM WALK ALGORITHMS FOR SOLVING INTEGRAL EQUATIONS * 8 CONVENTIONAL MONTE CARLO SCHEME * 8 BIASED ESTIMATORS * 14 LINEAR-FRACTIONAL TRANSFORMATIONS AND THEIR RELATIONS TO ITERATIVE PROCESSES * 16 ASYMPTOTICALLY UNBIASED ESTIMATORS BASED ON SINGULAR APPROXIMATIONS * 23 INTEGRAL EQUATION OF THE FIRST KIND * 30 RANDOM WALK-ON-BOUNDARY ALGORITHMS FOR THE LAPLACE EQUATION * 35 NEWTON POTENTIALS AND BOUNDARY INTEGRAL EQUATIONS OF THE ELECTROSTATICS * 35 THE INTERIOR DIRICHLET PROBLEM AND ISOTROPIC RANDOM WALK-ON-BOUNDARY PROCESS * 37 SOLUTION OF THE NEUMANN PROBLEM * 43 RANDOM ESTIMATORS FOR THE EXTERIOR DIRICHLET PROBLEM * 50 THIRD BVP AND ALTERNATIVE METHODS OF SOLVING THE DIRICHLET PROBLEM * 55 INHOMOGENEOUS PROBLEMS * 60 CONTINUITY BVP * 62 WALK ON BOUNDARY FOR THE CONTINUITY PROBLEM ---- 64 CALCULATION OF THE SOLUTION DERIVATIVES NEAR THE BOUNDARY ---- 65 NORMAL DERIVATIVE OF A DOUBLE-LAYER POTENTIAL * 69 WALK-ON-BOUNDARY ALGORITHMS FOR THE HEAT EQUATION * 72 HEAT POTENTIALS AND VOLTERRA BOUNDARY INTEGRAL EQUATIONS * 72 NONSTATIONARY WALK-ON-BOUNDARY PROCESS * 74 THE DIRICHLET PROBLEM * 77 THE NEUMANN PROBLEM * 80 THIRD BVP ---- 81 UNBIASEDNESS AND VARIANCE OF THE WALK-ON-BOUNDARY ALGORITHMS * 85 THE COST OF THE WALK-ON-BOUNDARY ALGORITHMS ---- 90 INHOMOGENEOUS HEAT EQUATION * 92 CALCULATION OF DERIVATIVES ON THE BOUNDARY * 94 5 5.1 5.2 5.3 6 6.1 6 . 1.1 6 . 1.2 6.2 6.3 6.4 6.5 7 7.1 7.2 7.3 7.4 7.4.1 7.4.2 7.4.3 7.5 7.5.1 7.6 8 8.1 8.2 8.3 8.3.1 8.3.2 SPATIAL PROBLEMS OF ELASTICITY * 99 ELASTOPOTENTIALS AND SYSTEMS OF BOUNDARY INTEGRAL EQUATIONS OF THE ELASTICITY THEORY ---- 99 FIRST BVP AND ESTIMATORS FOR SINGULAR INTEGRALS * 102 OTHER BVPS FOR THE LAME EQUATIONS AND REGULAR INTEGRAL EQUATIONS ---- 107 VARIANTS OF THE RANDOM WALK ON BOUNDARY FOR SOLVING STATIONARY POTENTIAL PROBLEMS * 110 THE ROBIN PROBLEM AND THE ERGODIC THEOREM * 110 MONTE CARLO ESTIMATOR FOR COMPUTING CAPACITANCE * 113 COMPUTING CHARGE DENSITY ---- 114 STATIONARY DIFFUSION EQUATION WITH ABSORPTION * 115 MULTIPLY CONNECTED DOMAINS ---- 116 STABILIZATION METHOD ---- 126 NONLINEAR POISSON EQUATION ---- 128 SPLITTING AND SURVIVAL PROBABILITIES IN RANDOM WALK METHODS AND APPLICATIONS * 131 INTRODUCTION * 131 SURVIVAL PROBABILITY FOR A SPHERE AND AN INTERVAL * 132 THE RECIPROCITY THEOREM FOR PARTICLE COLLECTION IN THE GENERAL CASE OF ROBIN BOUNDARY CONDITIONS ---- 135 SPLITTING AND SURVIVAL PROBABILITIES ---- 138 SPLITTING PROBABILITIES FOR A FINITE INTERVAL AND NANOWIRE GROWTH SIMULATION ---- 138 SURVIVAL PROBABILITY FOR A DISC AND THE EXTERIOR OF CIRCULAR CYLINDER ---- 140 SPLITTING PROBABILITIES FOR CONCENTRIC SPHERES AND ANNULUS * 141 CATHODOLUMINESCENCE * 145 THE RANDOM WOS AND HEMISPHERES ALGORITHM * 147 CONCLUSION AND DISCUSSION * 152 A RANDOM WOS-BASED KMC METHOD FOR ELECTRON-HOLE RECOMBINATIONS ---- 153 INTRODUCTION ---- 153 THE MEAN FIELD EQUATIONS ---- 155 MONTE CARLO ALGORITHMS ---- 157 RANDOM WOS FOR THE DIFFUSION SIMULATION ---- 157 RADIATIVE AND NONRADIATIVE RECOMBINATION IN THE ABSENCE OF DIFFUSION ---- 160 8.3.3 GENERAL CASE OF RADIATIVE AND NONRADIATIVE RECOMBINATION IN THE PRESENCE OF DIFFUSION * 161 8.4 SIMULATION RESULTS AND COMPARISON * 162 8.5 SUMMARY AND CONCLUSION * 165 9 MONTE CARLO METHODS FOR COMPUTING MACROMOLECULES PROPERTIES AND SOLVING RELATED PROBLEMS * 166 9.1 DIFFUSION-LIMITED REACTION RATE AND OTHER INTEGRAL PARAMETERS ---- 167 9.1.1 FORMULATION OF THE PROBLEM * 167 9.1.2 CAPACITANCE CALCULATIONS * 170 9.2 WALK IN SUBDOMAINS AND EFFICIENT SIMULATION OF BROWNIAN MOTION EXIT POINTS * 172 9.3 MONTE CARLO ALGORITHMS FOR BOUNDARY-VALUE CONDITIONS CONTAINING THE NORMAL DERIVATIVE * 174 9.3.1 WOS ALGORITHM FOR MIXED BOUNDARY-VALUE CONDITIONS * 174 9.3.2 MEAN-VALUE RELATION AT A POINT ON THE BOUNDARY * 176 9.3.3 CONSTRUCTION OF THE ALGORITHM AND ITS CONVERGENCE * 177 9.4 CONTINUITY BVP * 179 9.4.1 MONTE CARLO METHOD * 180 9.4.2 INTEGRAL REPRESENTATION AT A BOUNDARY POINT * 182 9.4.3 ESTIMATE FOR THE BOUNDARY VALUE * 184 9.4.4 CONSTRUCTION OF THE ALGORITHM AND ITS CONVERGENCE * 185 9.5 COMPUTING MACROMOLECULE ENERGY * 187 9.5.1 MATHEMATICAL MODEL AND COMPUTATIONAL RESULTS * 188 BIBLIOGRAPHY * 193
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author	Sabel'fel'd, Karl K. 1953- Simonov, Nikolai A.
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physical	ix, 198 Seiten 4 Diagramme 24 cm x 17 cm
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spellingShingle	Sabel'fel'd, Karl K. 1953- Simonov, Nikolai A. Stochastic methods for boundary value problems numerics for high-dimensional PDEs and applications Irrfahrtsproblem (DE-588)4162442-7 gnd Randwertproblem (DE-588)4048395-2 gnd Monte-Carlo-Simulation (DE-588)4240945-7 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd Integralgleichung (DE-588)4027229-1 gnd
subject_GND	(DE-588)4162442-7 (DE-588)4048395-2 (DE-588)4240945-7 (DE-588)4044779-0 (DE-588)4027229-1
title	Stochastic methods for boundary value problems numerics for high-dimensional PDEs and applications
title_auth	Stochastic methods for boundary value problems numerics for high-dimensional PDEs and applications
title_exact_search	Stochastic methods for boundary value problems numerics for high-dimensional PDEs and applications
title_full	Stochastic methods for boundary value problems numerics for high-dimensional PDEs and applications Karl K. Sabelfeld and Nikolai A. Simonov
title_fullStr	Stochastic methods for boundary value problems numerics for high-dimensional PDEs and applications Karl K. Sabelfeld and Nikolai A. Simonov
title_full_unstemmed	Stochastic methods for boundary value problems numerics for high-dimensional PDEs and applications Karl K. Sabelfeld and Nikolai A. Simonov
title_short	Stochastic methods for boundary value problems
title_sort	stochastic methods for boundary value problems numerics for high dimensional pdes and applications
title_sub	numerics for high-dimensional PDEs and applications
topic	Irrfahrtsproblem (DE-588)4162442-7 gnd Randwertproblem (DE-588)4048395-2 gnd Monte-Carlo-Simulation (DE-588)4240945-7 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd Integralgleichung (DE-588)4027229-1 gnd
topic_facet	Irrfahrtsproblem Randwertproblem Monte-Carlo-Simulation Partielle Differentialgleichung Integralgleichung
url	http://www.degruyter.com/search?f_0=isbnissn&q_0=9783110479065&searchTitles=true http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029177302&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT sabelfeldkarlk stochasticmethodsforboundaryvalueproblemsnumericsforhighdimensionalpdesandapplications AT simonovnikolaia stochasticmethodsforboundaryvalueproblemsnumericsforhighdimensionalpdesandapplications AT walterdegruytergmbhcokg stochasticmethodsforboundaryvalueproblemsnumericsforhighdimensionalpdesandapplications

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