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Efficient Legendre Spectral and Spectral Element Methods for Second-Order Problems with Diagonalization Technique
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DOI：10.1007/s10915-025-03048-z.png)
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Abstract
En 中文
Based on the diagonalization technique and matrix decomposition technique, a new series of Legendre basis functions is constructed, which are simultaneously orthogonal in both $$L^2$$ - and $$H^1$$ -inner products, and lead to diagonal systems for second-order problems. Then we construct efficient spectral and space-time spectral methods for multidimensional problems using Legendre approximation in space and Legendre-Gauss collocation method in time, which can be implemented in a synchronous parallel fashion. Meanwhile, a new Legendre spectral element methods for solving high oscillation or steep gradient solutions problems are proposed, which reduce the non-zero entries of linear systems and computational cost. Numerical experiments exhibit the effectiveness and accuracy of the suggested approaches.
Keywords:
Spectral methods
Spectral element methods
Simultaneously orthogonal Legendre basis functions
Multidimensional problems
Convergence analysis
Journal
IF:
3.3
Papers:
692
Citations:
9.6K