VMP Product and the Numerical Exploration of New Basis Functions

Key Points

• The aim is to construct orthogonal bases on distorted geometries using a VMP-induced inner product.
• Introduced a VMP-induced inner product for orthogonalization.
• Applied Gram-Schmidt process to enhance Gram matrix conditioning and reduce mode coupling.
• Used a homotopy to continuously recover classical L2 orthogonal systems.
• Improved orthogonal basis formations demonstrated through reproducible numerical examples.
• Achieved nearly block-diagonal structure post-orthogonalization.
• Demonstrated effectiveness in various distorted, non-orthogonal geometries.