A new parallel solver suited for arbitrary semilinear parabolic partial differential equations based on generalized random trees

DOI10.1016/j.jcp.2011.06.033zbMath1229.65005OpenAlexW2037755051MaRDI QIDQ648054

Ángel Rodríguez-Rozas, Juan A. Acebrón

Publication date: 22 November 2011

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jcp.2011.06.033

zbMATH Keywords

semilinear parabolic problemsnumerical examplesdomain decompositionMonte Carlo methodsparallel computingrandom treesfault-tolerant algorithmsinitial value semilinear parabolic problems

Mathematics Subject Classification ID

Random graphs (graph-theoretic aspects) (05C80) Monte Carlo methods (65C05) Parallel numerical computation (65Y05) Semilinear parabolic equations (35K58)

Related Items (10)

Stochastic Solutions of Nonlinear PDE’s and an Extension of Superprocesses ⋮ A Monte Carlo method for solving the one-dimensional telegraph equations with boundary conditions ⋮ Highly efficient numerical algorithm based on random trees for accelerating parallel Vlasov-Poisson simulations ⋮ Parallel stochastic methods for PDE based grid generation ⋮ Superprocesses on ultradistributions ⋮ A stochastic approach to the solution of magnetohydrodynamic equations ⋮ A highly parallel algorithm for computing the action of a matrix exponential on a vector based on a multilevel Monte Carlo method ⋮ Monte Carlo method for solution of initial-boundary value problem for nonlinear parabolic equations ⋮ The PDD method for solving linear, nonlinear, and fractional PDEs problems ⋮ Hybrid PDE solver for data-driven problems and modern branching

Cites Work

• Evaluation of conditional Wiener integrals by numerical integration of stochastic differential equations
• Efficient parallel solution of nonlinear parabolic partial differential equations by a probabilistic domain decomposition
• Domain decomposition solution of nonlinear two-dimensional parabolic problems by random trees
• Multivariate Fuss-Catalan numbers
• Higher-order implicit strong numerical schemes for stochastic differential equations
• Multiplicative cascades applied to PDEs (two numerical examples)
• The Padé approximant
• Probabilistically induced domain decomposition methods for elliptic boundary-value problems
• Convergence rate of the Sherman and Peskin branching stochastic particle method
• Functional Integration and Partial Differential Equations. (AM-109)
• Application of brownian motion to the equation of kolmogorov-petrovskii-piskunov
• Domain Decomposition Solution of Elliptic Boundary-Value Problems via Monte Carlo and Quasi-Monte Carlo Methods
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