4 papers
On the Pre-Asymptotic Stability and Inverse Structure of Extended-Domain Spectral Methods
Po-Yi Wu
The extended-domain method is a strategy for applying spectral methods to complex geometries. Its stability is complicated by the ill-conditioning of the Fourier extension frame. T…
Convergent Operator-Splitting Scheme for Viscosity Solutions: A Foundation for Learning Domain-to-Solution Maps
Po-Yi Wu
This work introduces and rigorously analyzes a novel operator-splitting finite element scheme for approximating viscosity solutions of a broad class of constrained second-order par…
A Projection Method for Compressible Generic Two-Fluid Model
Po-Yi Wu
A new projection method for a generic two-fluid model is presented in this work. Specifically, we extend the projection method, originally designed for single-phase variable densit…
Development of a New Spectral Collocation Method Using Laplacian Eigenbasis for Elliptic Partial Differential Equations in an Extended Domain
Po-Yi Wu, Cheng-Hong Robert Kao, Tony Wen-Hann Sheu
The recent development of spectral method has been praised for its high-order convergence in simulating complex physical problems. The combination of embedded boundary method and s…