68 citations · 127 across the 31 of their papers we have counts for
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A Reduced Radial Basis Function Method for Partial Differential Equations on irregular domains
Yanlai Chen, Sigal Gottlieb, Alfa Heryudono +1
We propose and test the first Reduced Radial Basis Function Method (RBFM) for solving parametric partial differential equations on irregular domains. The two major ingredients…
Parametric Analytical Preconditioning and its Applications to the Reduced Collocation Methods
Yanlai Chen, Sigal Gottlieb, Yvon Maday
In this paper, we extend the recently developed reduced collocation method \cite{ChenGottlieb} to the nonlinear case, and propose two analytical preconditioning strategies. One is…
Optimal Explicit Strong Stability Preserving Runge--Kutta Methods with High Linear Order and optimal Nonlinear Order
Sigal Gottlieb, Zachary J. Grant, Daniel Higgs
High order spatial discretizations with monotonicity properties are often desirable for the solution of hyperbolic PDEs. These methods can advantageously be coupled with high order…
A Fourier Pseudospectral Method for the "Good" Boussinesq Equation with Second Order Temporal Accuracy
Kelong Cheng, Wenqiang Feng, Sigal Gottlieb +1
In this paper, we discuss the nonlinear stability and convergence of a fully discrete Fourier pseudospectral method coupled with a specially designed second order time-stepping for…