A consistent approximate upwind Petrov—Galerkin method for convection-dominated problems
Computer Methods in Applied Mechanics and Engineering
A particle method for a scalar advection diffusion equation
Mathematics and Computers in Simulation
Computer Methods in Applied Mechanics and Engineering - Special edition on the 20th Anniversary
A multigrid tutorial: second edition
A multigrid tutorial: second edition
Runge-Kutta methods for Stratonovich stochastic differential equation systems with commutative noise
Journal of Computational and Applied Mathematics - Special Issue: Proceedings of the 10th international congress on computational and applied mathematics (ICCAM-2002)
A Fully Mass and Volume Conserving Implementation of a Characteristic Method for Transport Problems
SIAM Journal on Scientific Computing
Multigrid Techniques in Economics
Operations Research
| Hi-index | 31.45 |
A backward-in-time probabilistic method with spatial filter averaging is presented to solve linear second-order partial differential equations of the parabolic type. An advantage of this methodology is that while forward methods are subject to region with loss of density of particles and hence loss of spatial resolution of the solution, the solution given by backward methods is given on any desired grid. However, traditional backward time probabilistic method using Monte Carlo averaging are computationally expensive. We prove a convergence result and present several examples. The method leads to important improvement in computational efficiency and is expected to perform well to solve high dimensional problems where a solution is needed on a large grid.