Computing Exponential for Iterative Splitting Methods: Algorithms and Applications

[摘要] Iterative splitting methods have a huge amount to compute matrix exponential. Here, theacceleration and recovering of higher-order schemes can be achieved. From a theoretical point ofview, iterative splitting methods are at least alternating Picards fix-point iteration schemes. For practical applications, it is important to compute very fast matrix exponentials. In thispaper, we concentrate on developing fast algorithms to solve the iterative splitting scheme. First, we reformulate the iterative splitting scheme into an integral notation of matrix exponential. In this notation, we consider fast approximation schemes to the integral formulations,also known asϕ-functions. Second, the error analysis is explained and applied to the integralformulations. The novelty is to compute cheaply the decoupled exp-matrices and apply onlycheap matrix-vector multiplications for the higher-order terms. In general, we discuss an elegant way of embedding recently survey on methods for computingmatrix exponential with respect to iterative splitting schemes. We present numerical benchmark examples, that compared standard splitting schemeswith the higher-order iterative schemes. A real-life application in contaminant transport as atwo phase model is discussed and the fast computations of the operator splitting method isexplained.

[学科分类] 应用数学