耗散和波传播问题的高阶连续时间 Galerkin 高效并行解法

IF 4.3 3区材料科学 Q1 ENGINEERING, ELECTRICAL & ELECTRONIC

ACS Applied Electronic Materials Pub Date : 2024-06-19 DOI:10.1137/23m1572787

Zhiming Chen, Yong Liu

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引用次数: 0

摘要

SIAM 科学计算期刊》，第 46 卷第 3 期，第 A2073-A2100 页，2024 年 6 月。摘要。我们提出了针对耗散和波传播问题实现高阶连续时间 Galerkin 方法的高效并行算法。通过使用 Legendre 多项式作为形状函数，我们获得了刚度矩阵的特殊结构，从而可以扩展对角线 Padé 近似来求解带源项的常微分方程。我们证明了连续时间 Galerkin 方法的无条件稳定性、[数学] 误差估计和节点处的[数学] 超收敛性。数值实例证实了我们的理论结果。

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Efficient and Parallel Solution of High-Order Continuous Time Galerkin for Dissipative and Wave Propagation Problems

SIAM Journal on Scientific Computing, Volume 46, Issue 3, Page A2073-A2100, June 2024.
Abstract. We propose efficient and parallel algorithms for the implementation of the high-order continuous time Galerkin method for dissipative and wave propagation problems. By using Legendre polynomials as shape functions, we obtain a special structure of the stiffness matrix that allows us to extend the diagonal Padé approximation to solve ordinary differential equations with source terms. The unconditional stability, [math] error estimates, and [math] superconvergence at the nodes of the continuous time Galerkin method are proved. Numerical examples confirm our theoretical results.

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来源期刊

ACS Applied Electronic Materials Multiple-

CiteScore

7.20

自引率

4.30%

发文量

567