Mapped Multi-Patch Spectral Extreme Learning Machine for Partial Differential Equations

This paper studies Spectral-ELM, a fixed-feature solver that applies Chebyshev–Gauss–Lobatto differentiation matrices to nodal values of an extreme learning machine trial function. For partial differential equations on curved domains, it uses a mapped multi-patch formulation, represents curved quadrilateral patches as images of reference squares, and computes physical derivatives from associated metric terms.