From the 1 of 8 linked papers with an AI index.
8 papers
Performance Evaluation of Stabilized Corrections for Mixed Precision Runge--Kutta Methods
César Herrera, John Driscoll, Sigal Gottlieb +3
The paper numerically evaluates the runtime and accuracy of stabilized correction techniques for mixed‑precision diagonally implicit Runge‑Kutta methods applied to nonlinear PDEs,…
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…