Academic Journal
A direct PinT algorithm for higher-order nonlinear time-evolution equations.
| Τίτλος: | A direct PinT algorithm for higher-order nonlinear time-evolution equations. |
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| Συγγραφείς: | Zhong, Shun-Zhi1 (AUTHOR) szzhongm@sina.com, Zhao, Yong-Liang1 (AUTHOR) ylzhaofde@sina.com, Shu, Qian-Yu1 (AUTHOR) shuqy@sicnu.edu.cn |
| Πηγή: | Applied Numerical Mathematics. Sep2026, Vol. 227, p25-41. 17p. |
| Θεματικοί όροι: | *Nonlinear evolution equations, *Parallel algorithms, *Matrix decomposition, *Numerical analysis, *Autonomous differential equations, *Chebyshev polynomials, *Eigenanalysis |
| Περίληψη: | Higher-order nonlinear time-evolution equations have widespread applications in science and engineering, such as in solid mechanics, materials science, and fluid mechanics. We present a direct time-parallel methodology for the solution of time-dependent differential equations, ranging from first to third order. In contrast to traditional time-stepping methods, the core of our approach lies in directly solving the all-at-once system via diagonalization of the time discretization matrix B t applied to higher-order evolution equations. By the process of relating the characteristic equation to Chebyshev polynomials, we derive explicit expressions for the eigenvector matrix V of B t and its inverse V − 1. Our argument shows that C o n d 2 (V) = O (n 3) , where n denotes the total number of time steps. A direct parallel-in-time algorithm is designed by exploring the structure of the spectral decomposition of B t. Numerical experiments are provided to show the significant computational speedup of the proposed algorithm. [ABSTRACT FROM AUTHOR] |
| Βάση Δεδομένων: | Academic Search Index |
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