Journal ArticleDOI
ε-Shell error analysis for Walk On Spheres algorithms
Michael Mascagni,Chi-Ok Hwang +1 more
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TLDR
Empirical evidence and analytic analysis of the e-shell error in some simple boundary value problems for the Laplace and Poisson equations are presented and show that the error associated with thee-shell is O(e), for small e, supports the conclusion that GFFP is preferable to WOS in cases where both are applicable.About:
This article is published in Mathematics and Computers in Simulation.The article was published on 2003-06-10. It has received 27 citations till now. The article focuses on the topics: Monte Carlo method & Random walk.read more
Citations
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Journal ArticleDOI
The Capacitance of Pristine Ice Crystals and Aggregate Snowflakes
TL;DR: In this article, the trajectories of diffusing water molecules are directly sampled, using random walkers, by counting how many of these trajectories intersect the surface of the ice particle and how many escape outside a spherical boundary far from the particle.
Journal ArticleDOI
A Feynman-Kac path-integral implementation for Poisson's equation using an h -conditioned Green's function
TL;DR: This study presents a Feynman-Kac path-integral implementation for solving the Dirichlet problem for Poisson's equation that is a modified "walk on spheres" (WOS) that includes the Feynmans' path-Integral contribution for the source term.
Journal ArticleDOI
Exact solution for anisotropic diffusion-controlled reactions with partially reflecting conditions
TL;DR: A generalization of the model of Solc and Stockmayer to describe the diffusion-controlled reactions between chemically anisotropic reactants taking into account the partially reflecting conditions on two parts of the reaction surface is investigated.
Journal ArticleDOI
Fast Random Walk Based Capacitance Extraction for the 3-D IC Structures With Cylindrical Inter-Tier-Vias
TL;DR: A novel floating random walk (FRW) method is developed by rotating the transition cube to suit the cylindrical surface, devising a special space management technique, and proposing accelerating techniques for structures with large-sized through-silicon-vias, suggesting that the proposed techniques is up to hundreds times faster than a simple FRW approach and the boundary element method-based algorithms.
References
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Monte Carlo Methods
TL;DR: In this paper, the Monte Carlo method is not compelling for one dimensional integration, but it is more compelling for a d-dimensional integral evaluated withM points, so that the error in I goes down as 1/ √ M and is smaller if the variance σ 2 f of f is smaller.
Book
Partial differential equations
TL;DR: In this article, the authors focus on the quasilinear PDEs of second order, where the second derivatives of u appear in linear order only (i.e., in linear time).
Book
Functional Integration And Partial Differential Equations
TL;DR: The authors discusses some aspects of the theory of partial differential equations from the viewpoint of probability theory and provides results that have not previously appeared in book form, including research contributions of the author.
BookDOI
From Brownian motion to Schrödinger's equation
Kai Lai Chung,Chung-hsin Chao +1 more
TL;DR: In this paper, the case of one dimension is considered and the q-Green function is used to measure the number of vertices in the one-dimensional space of Brownian motion.