68 citations · 127 across the 31 of their papers we have counts for
32 papers
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…
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…
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…
A review of high order strong stability preserving two-derivative explicit, implicit, and IMEX methods
Sigal Gottlieb, Zachary J. Grant
High order strong stability preserving (SSP) time discretizations ensure the nonlinear non-inner-product strong stability properties of spatial discretizations suited for the stabl…
Toward exponentially-convergent simulations of extreme-mass-ratio inspirals: A time-domain solver for the scalar Teukolsky equation with singular source terms
Manas Vishal, Scott E. Field, Katie Rink +2
Gravitational wave signals from extreme mass ratio inspirals are a key target for space-based gravitational wave detectors. These systems are typically modeled as a distributionall…
Stability Analysis and Performance Evaluation of Mixed-Precision Runge-Kutta Methods
Ben Burnett, Sigal Gottlieb, Zachary J. Grant
Additive Runge-Kutta methods designed for preserving highly accurate solutions in mixed-precision computation were proposed and analyzed in 4. These specially designed methods use…
Discontinuous Galerkin method for linear wave equations involving derivatives of the Dirac delta distribution
Scott E. Field, Sigal Gottlieb, Gaurav Khanna +1
Linear wave equations sourced by a Dirac delta distribution and its derivative(s) can serve as a model for many different phenomena. We describe a discontinuous Galerkin (DG…
Performance Evaluation of Mixed-Precision Runge-Kutta Methods
Ben Burnett, Sigal Gottlieb, Zachary J. Grant +1
Additive Runge-Kutta methods designed for preserving highly accurate solutions in mixed-precision computation were proposed and analyzed in [8]. These specially designed methods us…
High order strong stability preserving multi-derivative implicit and IMEX Runge--Kutta methods with asymptotic preserving properties
Sigal Gottlieb, Zachary J. Grant, Jingwei Hu +1
In this work we present a class of high order unconditionally strong stability preserving (SSP) implicit multi-derivative Runge--Kutta schemes, and SSP implicit-explicit (IMEX) mul…
An EIM-degradation free reduced basis method via over collocation and residual hyper reduction-based error estimation
Yanlai Chen, Sigal Gottlieb, Lijie Ji +1
The need for multiple interactive, real-time simulations using different parameter values has driven the design of fast numerical algorithms with certifiable accuracies. The reduce…
A general linear method approach to the design and optimization of efficient, accurate, and easily implemented time-stepping methods in CFD
Victor DeCaria, Sigal Gottlieb, Zachary J. Grant +1
In simulations of fluid motion time accuracy has proven to be elusive. We seek highly accurate methods with strong enough stability properties to deal with the richness of scales o…
A GPU-accelerated mixed-precision WENO method for extremal black hole and gravitational wave physics computations
Scott E. Field, Sigal Gottlieb, Zachary J. Grant +2
We develop and use a novel mixed-precision weighted essentially non-oscillatory (WENO) method for solving the Teukolsky equation, which arises when modeling perturbations of Kerr b…
Two-derivative error inhibiting schemes with post-processing
Adi Ditkowski, Sigal Gottlieb, Zachary J. Grant
High order methods are often desired for the evolution of ordinary differential equations, in particular those arising from the semi-discretization of partial differential equation…
IMEX error inhibiting schemes with post-processing
Adi Ditkowski, Sigal Gottlieb, Zachary J. Grant
High order implicit-explicit (IMEX) methods are often desired when evolving the solution of an ordinary differential equation that has a stiff part that is linear and a non-stiff p…
Explicit and implicit error inhibiting schemes with post-processing
Adi Ditkowski, Sigal Gottlieb, Zachary J. Grant
Efficient high order numerical methods for evolving the solution of an ordinary differential equation are widely used. The popular Runge--Kutta methods, linear multi-step methods,…
L1-ROC and R2-ROC: L1- and R2-based Reduced Over-Collocation methods for parametrized nonlinear partial differential equations
Yanlai Chen, Sigal Gottlieb, Lijie Ji +2
The onerous task of repeatedly resolving certain parametrized partial differential equations (pPDEs) in, e.g. the optimization context, makes it imperative to design vastly more ef…
Strong Stability Preserving Integrating Factor Two-step Runge--Kutta Methods
Leah Isherwood, Zachary J. Grant, Sigal Gottlieb
Problems that feature significantly different time scales, where the stiff time-step restriction comes from a linear component, implicit-explicit (IMEX) methods alleviate this rest…
Downwinding for Preserving Strong Stability in Explicit Integrating Factor Runge--Kutta Methods
Leah Isherwood, Zachary J. Grant, Sigal Gottlieb
Strong stability preserving (SSP) Runge-Kutta methods are desirable when evolving in time problems that have discontinuities or sharp gradients and require nonlinear non-inner-prod…
A Strong Stability Preserving Analysis for Multistage Two-Derivative Time-Stepping Schemes Based on Taylor Series Conditions
Zachary Grant, Sigal Gottlieb, David C Seal
High order strong stability preserving (SSP) time discretizations are often needed to ensure the nonlinear (and sometimes non-inner-product) strong stability properties of spatial…
Strong Stability Preserving Integrating Factor Runge-Kutta Methods
Sigal Gottlieb, Zachary J. Grant, Leah Isherwood
Strong stability preserving (SSP) Runge-Kutta methods are often desired when evolving in time problems that have two components that have very different time scales. Where the SSP…
Implicit and Implicit-Explicit Strong Stability Preserving Runge-Kutta Methods with High Linear Order
Sidafa Conde, Sigal Gottlieb, Zachary J. Grant +1
When evolving in time the solution of a hyperbolic partial differential equation, it is often desirable to use high order strong stability preserving (SSP) time discretizations. Th…
Error Inhibiting Block One-Step Schemes for Ordinary Differential Equations
Adi Ditkowski, Sigal Gottlieb
The commonly used one step methods and linear multi-step methods all have a global error that is of the same order as the local truncation error (as defined in \cite{gustafsson1995…
Explicit Strong Stability Preserving Multistage Two-Derivative Time-Stepping Schemes
Andrew J. Christieb, Sigal Gottlieb, Zachary J. Grant +1
High order strong stability preserving (SSP) time discretizations are advantageous for use with spatial discretizations with nonlinear stability properties for the solution of hype…