Monte Carlo methods. Vol. 1: basics
Monte Carlo methods. Vol. 1: basics
A Monte Carlo method for scalar reaction diffusion equations
SIAM Journal on Scientific and Statistical Computing
A gradient random walk method for two-dimensional reaction-diffusion equations
SIAM Journal on Scientific Computing
On traveling wave solutions of Fisher's equation in two spatial dimensions
SIAM Journal on Applied Mathematics
Exponential Timestepping with Boundary Test for Stochastic Differential Equations
SIAM Journal on Scientific Computing
Sourcebook of parallel computing
Sourcebook of parallel computing
Introduction to Parallel Computing (Oxford Texts in Applied and Engineering Mathematics)
Introduction to Parallel Computing (Oxford Texts in Applied and Engineering Mathematics)
Simulation of stopped diffusions
Journal of Computational Physics
SIAM Journal on Scientific Computing
Multiplicative cascades applied to PDEs (two numerical examples)
Journal of Computational Physics
Probabilistically induced domain decomposition methods for elliptic boundary-value problems
Journal of Computational Physics
Supercomputing applications to the numerical modeling of industrial and applied mathematics problems
The Journal of Supercomputing
Domain decomposition solution of nonlinear two-dimensional parabolic problems by random trees
Journal of Computational Physics
A fully scalable parallel algorithm for solving elliptic partial differential equations
Euro-Par'07 Proceedings of the 13th international Euro-Par conference on Parallel Processing
Journal of Computational Physics
A stochastic approach to the solution of magnetohydrodynamic equations
Journal of Computational Physics
Journal of Computational Physics
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Initial- and initial-boundary value problems for nonlinear one-dimensional parabolic partial differential equations are solved numerically by a probabilistic domain decomposition method. This is based on a probabilistic representation of solutions by means of branching stochastic processes. Only few values of the solution inside the space-time domain are generated by a Monte Carlo method, and an interpolation is then made so to approximate suitable interfacial values of the solution inside the domain. In this way, a fully decoupled set of sub-problems is obtained. This method allows for an efficient massively parallel implementation, is scalable and fault tolerant. Numerical examples, including some for the KPP equation and beyond are given to show the performance of the algorithm.