Associate Professor Zhiguo Yang,Shanghai Jiao Tong University

Structure-preserving numerical methods are crucial for achieving long-time accurate, stable, consistent and physically meaningful simulations. In this talk, we present H^1 and H(div) conforming spectral bases with exact preservation of the incompressibility and magnetic Gauss’s law constraints for the incompressible and resistive magnetohydrodynamic (MHD) systems. Two key ingredients, i.e. exact de Rham complexes and their commuting diagram, and the derivative property of the generalized Jacobi polynomials, are essential for the derivation of the desired basis functions. We propose a fast matrix-free iterative solution algorithm based on the tensorial structure of the resultant linear system and a novel simultaneous multiple-matrices diagonalisation technique. This algorithm may serve as an essential building block for developing scalable high order spectral-element method for large-scale simulations. Ample 2D and 3D numerical examples illustrate both the accuracy and efficiency of the proposed method.