74 citations · 307 across the 16 of their papers we have counts for
18 papers
Spectral deferred correction methods for second-order problems
Ikrom Akramov, Sebastian Götschel, Michael Minion +2
Spectral deferred corrections (SDC) are a class of iterative methods for the numerical solution of ordinary differential equations. SDC can be interpreted as a Picard iteration to…
Exponential Runge-Kutta Parareal for Non-Diffusive Equations
Tommaso Buvoli, Michael L. Minion
Parareal is a well-known parallel-in-time algorithm that combines a coarse and fine propagator within a parallel iteration. It allows for large-scale parallelism that leads to sign…
On the Stability of Exponential Integrators for Non-Diffusive Equations
Tommaso Buvoli, Michael L. Minion
Exponential integrators are a well-known class of time integration methods that have been the subject of many studies and developments in the past two decades. Surprisingly, there…
Twelve Ways To Fool The Masses When Giving Parallel-In-Time Results
Sebastian Goetschel, Michael Minion, Daniel Ruprecht +1
Getting good speedup -- let alone high parallel efficiency -- for parallel-in-time (PinT) integration examples can be frustratingly difficult. The high complexity and large number…
IMEX Runge-Kutta Parareal for Non-Diffusive Equations
Tommaso Buvoli, Michael L. Minion
Parareal is a widely studied parallel-in-time method that can achieve meaningful speedup on certain problems. However, it is well known that the method typically performs poorly on…
An experimental comparison of a space-time multigrid method with PFASST for a reaction-diffusion problem
Pietro Benedusi, Michael Minion, Rolf Krause
We consider two parallel-in-time approaches applied to a (reaction) diffusion problem, possibly non-linear. In particular, we consider PFASST (Parallel Full Approximation Scheme in…
Improved Coupling of Hydrodynamics and Nuclear Reactions via Spectral Deferred Corrections
M. Zingale, M. P. Katz, J. B. Bell +3
Simulations in stellar astrophysics involve the coupling of hydrodynamics and nuclear reactions under a wide variety of conditions, from simmering convective flows to explosive nuc…
Parallel-in-Time Multi-Level Integration of the Shallow-Water Equations on the Rotating Sphere
Francois P. Hamon, Martin Schreiber, Michael L. Minion
The modeling of atmospheric processes in the context of weather and climate simulations is an important and computationally expensive challenge. The temporal integration of the und…
An Efficient Parallel-in-Time Method for Optimization with Parabolic PDEs
Sebastian Götschel, Michael L. Minion
To solve optimization problems with parabolic PDE constraints, often methods working on the reduced objective functional are used. They are computationally expensive due to the nec…
A Fourth-Order Adaptive Mesh Refinement Algorithm for the Multicomponent, Reacting Compressible Navier-Stokes Equations
Matthew Emmett, Emmanuel Motheau, Weiqun Zhang +2
In this paper we present a fourth-order in space and time block-structured adaptive mesh refinement algorithm for the compressible multicomponent reacting Navier-Stokes equations.…
Multi-Level Spectral Deferred Corrections Scheme for the Shallow Water Equations on the Rotating Sphere
Francois Hamon, Martin Schreiber, Michael Minion
Efficient time integration schemes are necessary to capture the complex processes involved in atmospheric flows over long periods of time. In this work, we propose a high-order, im…
Concurrent Implicit Spectral Deferred Correction Scheme for Low-Mach Number Combustion with Detailed Chemistry
Francois Hamon, Marcus Day, Michael Minion
We present a parallel implicit-explicit time integration scheme for the advection-diffusion-reaction systems arising from the equations governing low-Mach number combustion with co…
A high-order spectral deferred correction strategy for low Mach number flow with complex chemistry
Will Pazner, Andrew Nonaka, John Bell +2
We present a fourth-order finite-volume algorithm in space and time for low Mach number reacting flow with detailed kinetics and transport. Our temporal integration scheme is based…
Torsion and ground state maxima: close but not the same
Brian A. Benson, Richard S. Laugesen, Michael Minion +1
Could the location of the maximum point for a positive solution of a semilinear Poisson equation on a convex domain be independent of the form of the nonlinearity? Cima and Derrick…
Achieving algorithmic resilience for temporal integration through spectral deferred corrections
R. W. Grout, H. Kolla, M. L. Minion +1
Spectral deferred corrections (SDC) is an iterative approach for constructing higher- order accurate numerical approximations of ordinary differential equations. SDC starts with an…
Interweaving PFASST and Parallel Multigrid
Michael Minion, Robert Speck, Matthias Bolten +2
The parallel full approximation scheme in space and time (PFASST) introduced by Emmett and Minion in 2012 is an iterative strategy for the temporal parallelization of ODEs and disc…
Inexact spectral deferred corrections
Robert Speck, Daniel Ruprecht, Michael Minion +2
Spectral deferred correction (SDC) methods are an attractive approach to iteratively computing collocation solutions to an ODE by performing so-called sweeps with a low-order time…
A multi-level spectral deferred correction method
Robert Speck, Daniel Ruprecht, Matthew Emmett +3
The spectral deferred correction (SDC) method is an iterative scheme for computing a higher-order collocation solution to an ODE by performing a series of correction sweeps using a…