间断Galerkin方法的自动代码生成
Automated code generation for discontinuous Galerkin methods
摘要：
本文提出了一种从高阶输入生成低阶计算机代码的编译方法，用于求解间断伽辽金有限元形式。输入语言反映了传统的数学符号，编译器以标准程序设计语言生成有效的代码。这有利于快速生成有效的代码，在不同的空间维度的一般方程。阐述了编译器方法和计算机代码自动生成的关键概念。该方法是证明了一系列常见的问题，包括泊松，双调和，对流扩散和斯托克斯方程。
英文摘要：
A compiler approach for generating low-level computer code from high-level input for discontinuous Galerkin finite element forms is presented. The input language mirrors conventional mathematical notation, and the compiler generates efficient code in a standard programming language. This facilitates the rapid generation of efficient code for general equations in varying spatial dimensions. Key concepts underlying the compiler approach and the automated generation of computer code are elaborated. The approach is demonstrated for a range of common problems, including the Poisson, biharmonic, advection--diffusion and Stokes equations.
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