Jing Gao, Associate Professor, Xi’an Jiaotong University

Jialin Hong, Professor

Geometric spectral methods in multivariate domains

15:00-16:00 August 20(Thursday), N219

Stable and efficient spectral methods for time-dependent partial differential equations depend crucially on the choice of basis functions. This talk presents geometric spectral methods for multidimensional unit balls and triangular domains. We construct orthonormal systems whose differentiation matrices are skew-Hermitian, providing stability and preserving important structures such as dissipativity and mass conservation. The resulting methods also offer rapid convergence, fast coefficient computation, and efficient matrix operations. Numerical examples illustrate their accuracy and computational advantages, demonstrating a practical framework for structure-preserving spectral approximation on non-tensor-product domains.