To Be or Not to Be Intrusive? The Solution of Parametric and Stochastic Equations - the "Plain Vanilla" Galerkin Case
To Be or Not to Be Intrusive? The Solution of Parametric and Stochastic Equations - the "Plain Vanilla" Galerkin Case
复制标题
DOI：
10.1137/130942802
复制
发表时间：
2013-09
期刊：
影响因子：
--
通讯作者：
L. Giraldi;A. Litvinenko;Dishi Liu;H. Matthies;A. Nouy
中科院分区：
文献类型：
--
作者：
L. Giraldi;A. Litvinenko;Dishi Liu;H. Matthies;A. Nouy
在参数方程中——随机方程是一种特殊情况——人们可能希望近似解，以便于评估其对参数的依赖性。在参数中插入是一种明显的可能性——在这种情况下通常被称为搭配方法。在通常情况下，对于给定的固定参数值有一个“求解器”，这可以“非侵入式”地用作黑盒组件，以独立地计算所有插值点的解。通过扩展，所有其他方法，特别是产生某种耦合系统的简单Galerkin方法，通常被归类为“侵入式”。我们展示了对于这种“普通的”伽辽金公式，人们如何以非侵入的方式求解耦合系统，甚至最简单形式的块求解器也具有相当的效率。这至少为可能的加速打开了两种途径：第一，通过使用更复杂的块求解器从迭代中的耦合中受益；第二，……
In parametric equations---stochastic equations are a special case---one may want to approximate the solution such that it is easy to evaluate its dependence on the parameters. Interpolation in the parameters is an obvious possibility---in this context often labeled as a collocation method. In the frequent situation where one has a “solver” for a given fixed parameter value, this may be used “nonintrusively” as a black-box component to compute the solution at all the interpolation points independently of each other. By extension, all other methods, and especially simple Galerkin methods, which produce some kind of coupled system, are often classed as “intrusive.” We show how, for such “plain vanilla” Galerkin formulations, one may solve the coupled system in a nonintrusive way, and even the simplest form of block-solver has comparable efficiency. This opens at least two avenues for possible speed-up: first, to benefit from the coupling in the iteration by using more sophisticated block-solvers and, second,...