相关论文: Walk on Spheres Algorithm for Helmholtz and Yukawa…
Walk on Spheres algorithms leverage properties of Brownian Motion to create Monte Carlo estimates of solutions to a class of elliptic partial differential equations. We propose a new caching strategy which leverages the continuity of paths…
A discrete random walk method on grids was proposed and used to solve the linearized Poisson-Boltzmann equation (LPBE) \cite{Rammile}. Here, we present a new and efficient grid-free random walk method. Based on a modified `` Walk On…
We develop walk-on-sphere for fractional Poisson equations with Dirichilet boundary conditions in high dimensions. The walk-on-sphere method is based on probabilistic represen tation of the fractional Poisson equation. We propose effcient…
In [25] a Walk On Spheres (WOS) algorithm for Monte Carlo simulation of the solutions of the Yukawa and the Helmholtz PDE's was developed by using the so-called Duffin correspondence. In this paper we investigate the foundations behind the…
We present projected walk on spheres (PWoS), a novel pointwise and discretization-free Monte Carlo solver for surface PDEs with Dirichlet boundaries, as a generalization of the walk on spheres method (WoS) [Muller 1956; Sawhney and Crane…
Grid-free Monte Carlo methods based on the walk on spheres (WoS) algorithm solve fundamental partial differential equations (PDEs) like the Poisson equation without discretizing the problem domain or approximating functions in a finite…
In this paper, we present a stochastic method for the simulation of Laplace's equation with a mixed boundary condition in planar domains that are polygonal or bounded by circular arcs. We call this method the Reflected Walk-on-Spheres…
In this paper, we will present a new approach for solving Laplace equations in general 3-D domains. The approach is based on a local computation method for the DtN mapping of the Laplace equation by combining a deterministic (local)…
We introduce a Monte Carlo method for computing derivatives of the solution to a partial differential equation (PDE) with respect to problem parameters (such as domain geometry or boundary conditions). Derivatives can be evaluated at…
Solving elliptic partial differential equations (PDEs) is a fundamental step in various scientific and engineering studies. As a classic stochastic solver, the Walk-on-Spheres (WoS) method is a well-established and efficient algorithm that…
In this paper, using the approximate particular solutions of Helmholtz equations, we solve the boundary value problems of Helmholtz equations by combining the methods of fundamental solutions (MFS) with the methods of particular solutions…
We propose Neural Walk-on-Spheres (NWoS), a novel neural PDE solver for the efficient solution of high-dimensional Poisson equations. Leveraging stochastic representations and Walk-on-Spheres methods, we develop novel losses for neural…
We introduce the walk-on-boundary (WoB) method for solving boundary value problems to computer graphics. WoB is a grid-free Monte Carlo solver for certain classes of second order partial differential equations. A similar Monte Carlo solver,…
In the present paper, an algorithm for the numerical solution of the external Dirichlet generalized harmonic problem for a sphere by the method of probabilistic solution (MPS) is given, where generalized indicates that a boundary function…
The Initial-Boundary Value Problem for the heat equation is solved by using a new algorithm based on a random walk on heat balls. Even if it represents a sophisticated generalization of the Walk on Spheres (WOS) algorithm introduced to…
In this paper we examine the rate of convergence of one of the standard algorithms for emulating exit probabilities of Brownian motion, the Walk on Spheres (WoS) algorithm. We obtain the complete characterization of the rate of convergence…
In this paper, we prove that there exists a unique, bounded continuous weak solution to the Dirichlet boundary value problem for a general class of second-order elliptic operators with singular coefficients, which does not necessarily have…
This paper describes the application of the method of probabilistic solutions (MPS) to numerically solve the Dirichlet generalized and classical harmonic problems for irregular n sided pyramidal domains. Here, generalized means that the…
This paper is concerned with an inverse obstacle problem for the Laplace's equation. The aim is to recover the constant conductivity coefficient in the equation and the boundary of a Dirichlet polygonal obstacle from a single pair of Cauchy…
We propose a boundary integral formulation for the dynamic problem of electromagnetic scattering and transmission by homogeneous dielectric obstacles. In the spirit of Costabel and Stephan, we use the transmission conditions to reduce the…