1 citations · 1 across the 8 of their papers we have counts for
10 papers
A two-level preconditioner for discontinuous virtual element methods with irregular subdomains
Juan G. Calvo, César Herrera
We introduce and analyze a two-level overlapping additive Schwarz preconditioner for discontinuous Galerkin discretizations of virtual element spaces on general polygonal meshes in…
Efficient Shallow Ritz Method: 1D Semi-Linear Diffusion-Reaction and Allen-Cahn Equations
Zhiqiang Cai, César Herrera
An efficient shallow Ritz method was developed in [8, 9] for one-dimensional linear diffusion and diffusion-reaction problems. In this paper, the method is extended to a nonlinear…
Performance Evaluation of Stabilized Corrections for Mixed Precision Runge--Kutta Methods
César Herrera, John Driscoll, Sigal Gottlieb +3
Mixed precision Runge--Kutta methods reduce the cost of the expensive implicit solves in diagonally implicit Runge--Kutta (DIRK) schemes by evaluating them in low precision, while…
Structure-Guided Gauss-Newton Method: Linear Advection-Reaction Equation
Zhiqiang Cai, César Herrera
The least-squares neural network (LSNN) method introduced in [5] for linear advection-reaction equations is capable of accurately approximating discontinuous solutions without a pr…
Smooth perturbations of diagonally implicit Runge--Kutta methods
John Driscoll, Sigal Gottlieb, Zachary J. Grant +3
A mixed accuracy framework for Runge--Kutta methods presented in [Grant, JSC 2022] has been shown to speed up the computation in diagonally implicit Runge--Kutta (DIRK) methods by…
Stable corrections for perturbed diagonally implicit Runge--Kutta methods
John Driscoll, Sigal Gottlieb, Zachary J. Grant +4
A mixed accuracy framework for Runge--Kutta methods presented in Grant [JSC 2022] and applied to diagonally implicit Runge--Kutta (DIRK) methods can significantly speed up the comp…
Convergence Analysis of Block Newton Methods for 1D Shallow Neural Network Approximation
Zhiqiang Cai, Anastassia Doktorova, Robert D. Falgout +1
This paper analyzes local convergence of the block Newton (BN) method introduced in [5, 6] for one-dimensional shallow neural network approximation to functions and diffusion-react…
Mixed precision and mixed accuracy explicit two-derivative Runge--Kutta methods
Sigal Gottlieb, Zachary J. Grant, Cesar Herrera
Mixed precision Runge--Kutta methods have been recently developed and used for the time-evolution of partial differential equations. Two-derivative Runge--Kutta schemes may offer e…
Efficient Shallow Ritz Method For 1D Diffusion-Reaction Problems
Zhiqiang Cai, Anastassia Doktorova, Robert D. Falgout +1
This paper studies the shallow Ritz method for solving one-dimensional diffusion-reaction problems. The method is capable of improving the order of approximation for non-smooth pro…
Efficient Shallow Ritz Method For 1D Diffusion Problems
Zhiqiang Cai, Anastassia Doktorova, Robert D. Falgout +1
This paper studies the shallow Ritz method for solving the one-dimensional diffusion problem. It is shown that the shallow Ritz method improves the order of approximation dramatica…