Stochastic Methods for Boundary Value Problems :: Numerics for High-dimensional PDEs and Applications.
This monograph is devoted to random walk based stochastic algorithms for solving high-dimensional boundary value problems of mathematical physics and chemistry. It includes Monte Carlo methods where the random walks live not only on the boundary, but also inside the domain. A variety of examples fro...
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin/Boston, GERMANY :
De Gruyter,
2016.
©2016 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | This monograph is devoted to random walk based stochastic algorithms for solving high-dimensional boundary value problems of mathematical physics and chemistry. It includes Monte Carlo methods where the random walks live not only on the boundary, but also inside the domain. A variety of examples from capacitance calculations to electron dynamics in semiconductors are discussed to illustrate the viability of the approach. |
| Beschreibung: | 1 online resource (208) |
| Bibliographie: | Includes bibliographical references. |
| ISBN: | 3110479451 9783110479454 |
Internformat
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| 100 | 1 | |a Sabelfeld, Karl K. | |
| 245 | 1 | 0 | |a Stochastic Methods for Boundary Value Problems : |b Numerics for High-dimensional PDEs and Applications. |
| 260 | |a Berlin/Boston, GERMANY : |b De Gruyter, |c 2016. | ||
| 264 | 4 | |c ©2016 | |
| 300 | |a 1 online resource (208) | ||
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| 505 | 0 | |a 1 Introduction ; 2 Random walk algorithms for solving integral equations ; 2.1 Conventional Monte Carlo scheme ; 2.2 Biased estimators ; 2.3 Linear-fractional transformations and their relations to iterative processes. | |
| 505 | 8 | |a 2.4 Asymptotically unbiased estimators based on singular approximations 2.5 Integral equation of the first kind ; 3 Random walk-on-boundary algorithms for the Laplace equation ; 3.1 Newton potentials and boundary integral equations of the electrostatics. | |
| 505 | 8 | |a 3.2 The interior Dirichlet problem and isotropic random walk-on-boundary process 3.3 Solution of the Neumann problem ; 3.4 Random estimators for the exterior Dirichlet problem ; 3.5 Third BVP and alternative methods of solving the Dirichlet problem ; 3.6 Inhomogeneous problems. | |
| 505 | 8 | |a 3.7 Continuity BVP 3.7.1 Walk on boundary for the continuity problem ; 3.8 Calculation of the solution derivatives near the boundary ; 3.9 Normal derivative of a double-layer potential ; 4 Walk-on-boundary algorithms for the heat equation. | |
| 505 | 8 | |a 4.1 Heat potentials and Volterra boundary integral equations 4.2 Nonstationary walk-on-boundary process ; 4.3 The Dirichlet problem ; 4.4 The Neumann problem ; 4.5 Third BVP ; 4.6 Unbiasedness and variance of the walk-on-boundary algorithms. | |
| 504 | |a Includes bibliographical references. | ||
| 520 | |a This monograph is devoted to random walk based stochastic algorithms for solving high-dimensional boundary value problems of mathematical physics and chemistry. It includes Monte Carlo methods where the random walks live not only on the boundary, but also inside the domain. A variety of examples from capacitance calculations to electron dynamics in semiconductors are discussed to illustrate the viability of the approach. | ||
| 546 | |a In English. | ||
| 650 | 0 | |a Boundary value problems |x Numerical solutions. |0 http://id.loc.gov/authorities/subjects/sh85016105 | |
| 650 | 0 | |a Stochastic analysis. |0 http://id.loc.gov/authorities/subjects/sh85128175 | |
| 650 | 0 | |a Random walks (Mathematics) |0 http://id.loc.gov/authorities/subjects/sh85111357 | |
| 650 | 6 | |a Problèmes aux limites |x Solutions numériques. | |
| 650 | 6 | |a Analyse stochastique. | |
| 650 | 6 | |a Marches aléatoires (Mathématiques) | |
| 650 | 7 | |a MATHEMATICS |x Applied. |2 bisacsh | |
| 650 | 7 | |a MATHEMATICS |x Probability & Statistics |x General. |2 bisacsh | |
| 650 | 7 | |a Boundary value problems |x Numerical solutions |2 fast | |
| 650 | 7 | |a Random walks (Mathematics) |2 fast | |
| 650 | 7 | |a Stochastic analysis |2 fast | |
| 650 | 7 | |a Partielle Differentialgleichung |2 gnd |0 http://d-nb.info/gnd/4044779-0 | |
| 650 | 7 | |a Integralgleichung |2 gnd |0 http://d-nb.info/gnd/4027229-1 | |
| 650 | 7 | |a Randwertproblem |2 gnd |0 http://d-nb.info/gnd/4048395-2 | |
| 650 | 7 | |a Monte-Carlo-Simulation |2 gnd |0 http://d-nb.info/gnd/4240945-7 | |
| 650 | 7 | |a Irrfahrtsproblem |2 gnd |0 http://d-nb.info/gnd/4162442-7 | |
| 700 | 1 | |a Simonov, N. A. |1 https://id.oclc.org/worldcat/entity/E39PCjrQrfr4fYrwGjWHGPM96q |0 http://id.loc.gov/authorities/names/n91005632 | |
| 758 | |i has work: |a Stochastic methods for boundary value problems (Text) |1 https://id.oclc.org/worldcat/entity/E39PCGHDjRdJXCJ37MJfCW9xDq |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
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Datensatz im Suchindex
| DE-BY-FWS_katkey | ZDB-4-EBA-ocn960040322 |
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| _version_ | 1816882364363571200 |
| adam_text | |
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| author | Sabelfeld, Karl K. |
| author2 | Simonov, N. A. |
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| author_GND | http://id.loc.gov/authorities/names/n91005632 |
| author_facet | Sabelfeld, Karl K. Simonov, N. A. |
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| contents | 1 Introduction ; 2 Random walk algorithms for solving integral equations ; 2.1 Conventional Monte Carlo scheme ; 2.2 Biased estimators ; 2.3 Linear-fractional transformations and their relations to iterative processes. 2.4 Asymptotically unbiased estimators based on singular approximations 2.5 Integral equation of the first kind ; 3 Random walk-on-boundary algorithms for the Laplace equation ; 3.1 Newton potentials and boundary integral equations of the electrostatics. 3.2 The interior Dirichlet problem and isotropic random walk-on-boundary process 3.3 Solution of the Neumann problem ; 3.4 Random estimators for the exterior Dirichlet problem ; 3.5 Third BVP and alternative methods of solving the Dirichlet problem ; 3.6 Inhomogeneous problems. 3.7 Continuity BVP 3.7.1 Walk on boundary for the continuity problem ; 3.8 Calculation of the solution derivatives near the boundary ; 3.9 Normal derivative of a double-layer potential ; 4 Walk-on-boundary algorithms for the heat equation. 4.1 Heat potentials and Volterra boundary integral equations 4.2 Nonstationary walk-on-boundary process ; 4.3 The Dirichlet problem ; 4.4 The Neumann problem ; 4.5 Third BVP ; 4.6 Unbiasedness and variance of the walk-on-boundary algorithms. |
| ctrlnum | (OCoLC)960040322 |
| dewey-full | 519.2/3 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.2/3 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| id | ZDB-4-EBA-ocn960040322 |
| illustrated | Not Illustrated |
| indexdate | 2024-11-27T13:27:26Z |
| institution | BVB |
| isbn | 3110479451 9783110479454 |
| language | English |
| oclc_num | 960040322 |
| open_access_boolean | |
| owner | MAIN DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (208) |
| psigel | ZDB-4-EBA |
| publishDate | 2016 |
| publishDateSearch | 2016 |
| publishDateSort | 2016 |
| publisher | De Gruyter, |
| record_format | marc |
| spelling | Sabelfeld, Karl K. Stochastic Methods for Boundary Value Problems : Numerics for High-dimensional PDEs and Applications. Berlin/Boston, GERMANY : De Gruyter, 2016. ©2016 1 online resource (208) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Print version record. 1 Introduction ; 2 Random walk algorithms for solving integral equations ; 2.1 Conventional Monte Carlo scheme ; 2.2 Biased estimators ; 2.3 Linear-fractional transformations and their relations to iterative processes. 2.4 Asymptotically unbiased estimators based on singular approximations 2.5 Integral equation of the first kind ; 3 Random walk-on-boundary algorithms for the Laplace equation ; 3.1 Newton potentials and boundary integral equations of the electrostatics. 3.2 The interior Dirichlet problem and isotropic random walk-on-boundary process 3.3 Solution of the Neumann problem ; 3.4 Random estimators for the exterior Dirichlet problem ; 3.5 Third BVP and alternative methods of solving the Dirichlet problem ; 3.6 Inhomogeneous problems. 3.7 Continuity BVP 3.7.1 Walk on boundary for the continuity problem ; 3.8 Calculation of the solution derivatives near the boundary ; 3.9 Normal derivative of a double-layer potential ; 4 Walk-on-boundary algorithms for the heat equation. 4.1 Heat potentials and Volterra boundary integral equations 4.2 Nonstationary walk-on-boundary process ; 4.3 The Dirichlet problem ; 4.4 The Neumann problem ; 4.5 Third BVP ; 4.6 Unbiasedness and variance of the walk-on-boundary algorithms. Includes bibliographical references. This monograph is devoted to random walk based stochastic algorithms for solving high-dimensional boundary value problems of mathematical physics and chemistry. It includes Monte Carlo methods where the random walks live not only on the boundary, but also inside the domain. A variety of examples from capacitance calculations to electron dynamics in semiconductors are discussed to illustrate the viability of the approach. In English. Boundary value problems Numerical solutions. http://id.loc.gov/authorities/subjects/sh85016105 Stochastic analysis. http://id.loc.gov/authorities/subjects/sh85128175 Random walks (Mathematics) http://id.loc.gov/authorities/subjects/sh85111357 Problèmes aux limites Solutions numériques. Analyse stochastique. Marches aléatoires (Mathématiques) MATHEMATICS Applied. bisacsh MATHEMATICS Probability & Statistics General. bisacsh Boundary value problems Numerical solutions fast Random walks (Mathematics) fast Stochastic analysis fast Partielle Differentialgleichung gnd http://d-nb.info/gnd/4044779-0 Integralgleichung gnd http://d-nb.info/gnd/4027229-1 Randwertproblem gnd http://d-nb.info/gnd/4048395-2 Monte-Carlo-Simulation gnd http://d-nb.info/gnd/4240945-7 Irrfahrtsproblem gnd http://d-nb.info/gnd/4162442-7 Simonov, N. A. https://id.oclc.org/worldcat/entity/E39PCjrQrfr4fYrwGjWHGPM96q http://id.loc.gov/authorities/names/n91005632 has work: Stochastic methods for boundary value problems (Text) https://id.oclc.org/worldcat/entity/E39PCGHDjRdJXCJ37MJfCW9xDq https://id.oclc.org/worldcat/ontology/hasWork Print version: 9783110479065 3110479060 (DLC) 2016042706 (OCoLC)949750711 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=1362724 Volltext |
| spellingShingle | Sabelfeld, Karl K. Stochastic Methods for Boundary Value Problems : Numerics for High-dimensional PDEs and Applications. 1 Introduction ; 2 Random walk algorithms for solving integral equations ; 2.1 Conventional Monte Carlo scheme ; 2.2 Biased estimators ; 2.3 Linear-fractional transformations and their relations to iterative processes. 2.4 Asymptotically unbiased estimators based on singular approximations 2.5 Integral equation of the first kind ; 3 Random walk-on-boundary algorithms for the Laplace equation ; 3.1 Newton potentials and boundary integral equations of the electrostatics. 3.2 The interior Dirichlet problem and isotropic random walk-on-boundary process 3.3 Solution of the Neumann problem ; 3.4 Random estimators for the exterior Dirichlet problem ; 3.5 Third BVP and alternative methods of solving the Dirichlet problem ; 3.6 Inhomogeneous problems. 3.7 Continuity BVP 3.7.1 Walk on boundary for the continuity problem ; 3.8 Calculation of the solution derivatives near the boundary ; 3.9 Normal derivative of a double-layer potential ; 4 Walk-on-boundary algorithms for the heat equation. 4.1 Heat potentials and Volterra boundary integral equations 4.2 Nonstationary walk-on-boundary process ; 4.3 The Dirichlet problem ; 4.4 The Neumann problem ; 4.5 Third BVP ; 4.6 Unbiasedness and variance of the walk-on-boundary algorithms. Boundary value problems Numerical solutions. http://id.loc.gov/authorities/subjects/sh85016105 Stochastic analysis. http://id.loc.gov/authorities/subjects/sh85128175 Random walks (Mathematics) http://id.loc.gov/authorities/subjects/sh85111357 Problèmes aux limites Solutions numériques. Analyse stochastique. Marches aléatoires (Mathématiques) MATHEMATICS Applied. bisacsh MATHEMATICS Probability & Statistics General. bisacsh Boundary value problems Numerical solutions fast Random walks (Mathematics) fast Stochastic analysis fast Partielle Differentialgleichung gnd http://d-nb.info/gnd/4044779-0 Integralgleichung gnd http://d-nb.info/gnd/4027229-1 Randwertproblem gnd http://d-nb.info/gnd/4048395-2 Monte-Carlo-Simulation gnd http://d-nb.info/gnd/4240945-7 Irrfahrtsproblem gnd http://d-nb.info/gnd/4162442-7 |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85016105 http://id.loc.gov/authorities/subjects/sh85128175 http://id.loc.gov/authorities/subjects/sh85111357 http://d-nb.info/gnd/4044779-0 http://d-nb.info/gnd/4027229-1 http://d-nb.info/gnd/4048395-2 http://d-nb.info/gnd/4240945-7 http://d-nb.info/gnd/4162442-7 |
| 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. |
| title_fullStr | Stochastic Methods for Boundary Value Problems : Numerics for High-dimensional PDEs and Applications. |
| title_full_unstemmed | Stochastic Methods for Boundary Value Problems : Numerics for High-dimensional PDEs and Applications. |
| 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 | Boundary value problems Numerical solutions. http://id.loc.gov/authorities/subjects/sh85016105 Stochastic analysis. http://id.loc.gov/authorities/subjects/sh85128175 Random walks (Mathematics) http://id.loc.gov/authorities/subjects/sh85111357 Problèmes aux limites Solutions numériques. Analyse stochastique. Marches aléatoires (Mathématiques) MATHEMATICS Applied. bisacsh MATHEMATICS Probability & Statistics General. bisacsh Boundary value problems Numerical solutions fast Random walks (Mathematics) fast Stochastic analysis fast Partielle Differentialgleichung gnd http://d-nb.info/gnd/4044779-0 Integralgleichung gnd http://d-nb.info/gnd/4027229-1 Randwertproblem gnd http://d-nb.info/gnd/4048395-2 Monte-Carlo-Simulation gnd http://d-nb.info/gnd/4240945-7 Irrfahrtsproblem gnd http://d-nb.info/gnd/4162442-7 |
| topic_facet | Boundary value problems Numerical solutions. Stochastic analysis. Random walks (Mathematics) Problèmes aux limites Solutions numériques. Analyse stochastique. Marches aléatoires (Mathématiques) MATHEMATICS Applied. MATHEMATICS Probability & Statistics General. Boundary value problems Numerical solutions Stochastic analysis Partielle Differentialgleichung Integralgleichung Randwertproblem Monte-Carlo-Simulation Irrfahrtsproblem |
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| work_keys_str_mv | AT sabelfeldkarlk stochasticmethodsforboundaryvalueproblemsnumericsforhighdimensionalpdesandapplications AT simonovna stochasticmethodsforboundaryvalueproblemsnumericsforhighdimensionalpdesandapplications |