论文标题
多物理系统解决方案中数值错误的后验估计
Goal-oriented a posteriori estimation of numerical errors in the solution of multiphysics systems
论文作者
论文摘要
本文开发了一种通用方法，用于在时间依赖性多物理数值模拟中进行后验误差估计。该方法基于广义结构添加剂runge-kutta（gark）时间集成方法。 Gark提供了多方法的统一公式，该公式通过将不同的离散公式和/或不同的时间步骤应用于系统的各个组件来模拟复杂系统。我们得出离散的天窗伴随并分析其时间准确性。基于伴随方法，我们为时间和空间离散误差对给定目标函数的影响建立了可计算的后验身份。用反应扩散系统的数值示例说明了衍生误差度量的准确性。局部误差分解用于说明该框架在时间和空间网格的自适应改进中的功能。
This paper develops a general methodology for a posteriori error estimation in time-dependent multiphysics numerical simulations. The methodology builds upon the generalized-structure additive Runge--Kutta (GARK) approach to time integration. GARK provides a unified formulation of multimethods that simulate complex systems by applying different discretization formulas and/or different time steps to individual components of the system. We derive discrete GARK adjoints and analyze their time accuracy. Based on the adjoint method, we establish computable a posteriori identities for the impacts of both temporal and spatial discretization errors on a given goal function. Numerical examples with reaction-diffusion systems illustrate the accuracy of the derived error measures. Local error decompositions are used to illustrate the power of this framework in adaptive refinements of both temporal and spatial meshes.
