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We propose and test the Reduced Meshless Collocation Method for solving parametric partial differential equations on irregular domains. The two major ingredients are meshless collocation method based on radial basis function (RBF) in finite difference mode solver and a collocation-based model reduction approach that systematically generates a reduced-order approximation whose dimension is orders of magnitude smaller than the total number of RBF centers. The resulting algorithm is demonstrated through two- and three-dimensional test problems. This is a joint work with Yanlai Chen, Sigal Gottlieb, and Akil Narayan at UMass Dartmouth.

radial basis function, reduced basis method, collocation, numerical PDEs