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The first passage time is then represented explicitly.\nThe method can easily be implemented to solve diffusion problems with spatially varying diffusion\ncoefficients for complicated three-dimensional domains. Particle tracking algorithm is highly efficient for calculation of fluxes to boundaries. We apply the developed algorithm for solving an exciton transport in a semiconductor material with a threading dislocation\nwhere the measured functions are the exciton fluxes to the semiconductor\u2019s substrate and on the dislocation surface.<\/jats:p>","DOI":"10.1515\/mcma-2023-2022","type":"journal-article","created":{"date-parts":[[2023,11,14]],"date-time":"2023-11-14T10:41:38Z","timestamp":1699958498000},"page":"73-80","source":"Crossref","is-referenced-by-count":0,"title":["Random walk on spheres method for solving anisotropic transient diffusion problems and flux calculations"],"prefix":"10.1515","volume":"30","author":[{"given":"Irina","family":"Shalimova","sequence":"first","affiliation":[{"name":"Institute of Computational Mathematics and Mathematical Geophysics , Russian Academy of Sciences , Novosibirsk , Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3698-7540","authenticated-orcid":false,"given":"Karl","family":"Sabelfeld","sequence":"additional","affiliation":[{"name":"Institute of Computational Mathematics and Mathematical Geophysics , Russian Academy of Sciences , Novosibirsk , Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2023,11,15]]},"reference":[{"key":"2024022618254292180_j_mcma-2023-2022_ref_001","doi-asserted-by":"crossref","unstructured":"O.  Brandt, V. M.  Kaganer, J.  L\u00e4hnemann, T.  Flissikowski, C.  Pf\u00fcller, K. K.  Sabelfeld, A. E.  Kireeva, C.  Cheze, R.  Calarco, H.  Grahn and U.  Jahn,\nCarrier diffusion in GaN: A cathodoluminescence study. II: Ambipolar versus exciton diffusion,\nPhys. Rev. Appl. 17 (2022), no. 2, Article ID 024018.","DOI":"10.1103\/PhysRevApplied.17.024018"},{"key":"2024022618254292180_j_mcma-2023-2022_ref_002","doi-asserted-by":"crossref","unstructured":"L.  Devroye,\nThe series method for random variate generation and its application to the Kolmogorov\u2013Smirnov distribution,\nAmer. J. Math. Manag. Sci. 1 (1981), no. 4, 359\u2013379.","DOI":"10.1080\/01966324.1981.10737080"},{"key":"2024022618254292180_j_mcma-2023-2022_ref_003","doi-asserted-by":"crossref","unstructured":"A.  Donev, V. V.  Bulatov, T.  Oppelstrup, G. H.  Gilmer, B.  Sadigh and M. H.  Kalos,\nA first-passage kinetic Monte Carlo algorithm for complex diffusion-reaction systems,\nJ. Comput. Phys. 229 (2010), no. 9, 3214\u20133236.","DOI":"10.1016\/j.jcp.2009.12.038"},{"key":"2024022618254292180_j_mcma-2023-2022_ref_004","doi-asserted-by":"crossref","unstructured":"J. A.  Given, J. B.  Hubbard and J. F.  Douglas,\nA first-passage algorithm for the hydrodynamic friction and diffusion-limited reaction rate of macromolecules,\nJ. Chem. Phys. 106 (1997), no. 9, 3761\u20133771.","DOI":"10.1063\/1.473428"},{"key":"2024022618254292180_j_mcma-2023-2022_ref_005","doi-asserted-by":"crossref","unstructured":"A.  Haji-Sheikh and E. M.  Sparrow,\nThe floating random walk and its application to Monte Carlo solutions of heat equations,\nSIAM J. Appl. Math. 14 (1966), 370\u2013389.","DOI":"10.1137\/0114031"},{"key":"2024022618254292180_j_mcma-2023-2022_ref_006","doi-asserted-by":"crossref","unstructured":"P.  Irkhin and I.  Biaggio,\nDirect imaging of anisotropic exciton diffusion and triplet diffusion length in rubrene single crystals,\nPhys. Rev. Lett. 107 (2011), no. 1, Article ID 017402.","DOI":"10.1103\/PhysRevLett.107.017402"},{"key":"2024022618254292180_j_mcma-2023-2022_ref_007","doi-asserted-by":"crossref","unstructured":"U.  Jahn, V. M.  Kaganer, K. K.  Sabelfeld, A. E.  Kireeva, J.  L\u00e4hnemann, C.  Pf\u00fcller, C.  Cheze, K.  Biermann, R.  Calarco and O.  Brandt,\nCarrier diffusion in GaN: A cathodoluminescence study. I: Temperature-dependent generation volume,\nPhys. Rev. Appl. 17 (2022), no. 2, Article ID 024017.","DOI":"10.1103\/PhysRevApplied.17.024017"},{"key":"2024022618254292180_j_mcma-2023-2022_ref_008","doi-asserted-by":"crossref","unstructured":"V. M.  Kaganer, J.  L\u00e4hnemann, C.  Pf\u00fcller, K. K.  Sabelfeld, A. E.  Kireeva and O.  Brandt,\nDetermination of the carrier diffusion length in GaN from cathodoluminescence maps around threading dislocations: Fallacies and opportunities,\nPhys. Rev. Appl. 12 (2019), Article ID 054038.","DOI":"10.1103\/PhysRevApplied.12.054038"},{"key":"2024022618254292180_j_mcma-2023-2022_ref_009","doi-asserted-by":"crossref","unstructured":"V. M.  Kaganer, K. K.  Sabelfeld and O.  Brandt,\nPiezoelectric field, exciton lifetime, and cathodoluminescence intensity at threading dislocations in GaN0001,\nAppl. Phys. Lett. 112 (2018), no. 12, Article ID 122101.","DOI":"10.1063\/1.5022170"},{"key":"2024022618254292180_j_mcma-2023-2022_ref_010","doi-asserted-by":"crossref","unstructured":"J.  L\u00e4hnemann, V. M.  Kaganer, K. K.  Sabelfeld, A. E.  Kireeva, U.  Jahn, C.  Cheze, R.  Calarco and O.  Brandt,\nCarrier diffusion in GaN: A cathodoluminescence study. III: Nature of nonradiative recombination at threading dislocations,\nPhys Rev. Appl. 17 (2022), no. 2, Article ID 024019.","DOI":"10.1103\/PhysRevApplied.17.024019"},{"key":"2024022618254292180_j_mcma-2023-2022_ref_011","doi-asserted-by":"crossref","unstructured":"W.  Liu, J. F.  Carlin, N.  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