HIGH ORDER INTEGRATOR FOR SAMPLING THE INVARIANT DISTRIBUTION OF A CLASS OF PARABOLIC STOCHASTIC PDES WITH ADDITIVE SPACE-TIME NOISE

被引：18

作者：

Brehier, Charles-Edouard ^{[1
]}

Vilmart, Gilles ^{[2
]}

机构：

[1] Univ Lyon 1, Inst Camille Jordan, CNRS UMR 5208, 43 Blvd 11 Novembre 1918, F-69622 Villeurbanne, France

[2] Univ Geneva, Sect Math, 2-4 Rue Lievre,CP 64, CH-1211 Geneva 4, Switzerland

来源：

SIAM JOURNAL ON SCIENTIFIC COMPUTING | 2016年 / 38卷 / 04期

基金：

瑞士国家科学基金会;

关键词：

stochastic partial differential equations; postprocessor; invariant measure; ergodicity; space-time white noise; PARTIAL-DIFFERENTIAL-EQUATIONS; MEAN-SQUARE STABILITY; RUNGE-KUTTA METHODS; NUMERICAL APPROXIMATION; WEAK APPROXIMATION; ERGODIC SDES; SPDES; SYSTEMS; ACCURACY; SCHEMES;

D O I：

10.1137/15M1021088

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We introduce a time-integrator to sample with high order of accuracy the invariant distribution for a class of semilinear stochastic PDEs (SPDEs) driven by an additive space-time noise. Combined with a postprocessor, the new method is a modification with negligible overhead of the standard linearized implicit Euler-Maruyama method. We first provide an analysis of the integrator when applied for SDEs (finite dimension), where we prove that the method has order 2 for the approximation of the invariant distribution, instead of 1. We then perform a stability analysis of the integrator in the semilinear SPDE context, and we prove in a linear case that a higher order of convergence is achieved. Numerical experiments, including the semilinear heat equation driven by space-time white noise, confirm the theoretical findings and illustrate the efficiency of the approach.

引用

页码：A2283 / A2306

页数：24

共 38 条

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