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Related papers: Inexact spectral deferred corrections

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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 low-order timestepping method. This paper examines a…

Numerical Analysis · Mathematics 2015-10-09 Robert Speck , Daniel Ruprecht , Matthew Emmett , Michael Minion , Matthias Bolten , Rolf Krause

Spectral deferred corrections (SDC) is an iterative approach for constructing higher- order accurate numerical approximations of ordinary differential equations. SDC starts with an initial approximation of the solution defined at a set of…

Computational Engineering, Finance, and Science · Computer Science 2017-06-14 R. W. Grout , H. Kolla , M. L. Minion , J. B. Bell

The spectral deferred correction (SDC) method is class of iterative solvers for ordinary differential equations (ODEs). It can be interpreted as a preconditioned Picard iteration for the collocation problem. The convergence of this method…

Numerical Analysis · Mathematics 2021-11-03 Gitte Kremling , Robert Speck

Spectral Deferred Correction (SDC) is an iterative method for the numerical solution of ordinary differential equations. It works by refining the numerical solution for an initial value problem by approximately solving differential…

Numerical Analysis · Mathematics 2025-09-09 Thomas Saupe , Sebastian Götschel , Thibaut Lunet , Daniel Ruprecht , Robert Speck

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 solve a fully implicit collocation problem, preconditioned…

Numerical Analysis · Mathematics 2024-05-15 Ikrom Akramov , Sebastian Götschel , Michael Minion , Daniel Ruprecht , Robert Speck

In this work we analyze the convergence properties of the Spectral Deferred Correction (SDC) method originally proposed by Dutt et al. [BIT, 40 (2000), pp. 241--266]. The framework for this high-order ordinary differential equation (ODE)…

Numerical Analysis · Mathematics 2019-07-24 Mathew F. Causley , David C. Seal

In this paper we present two strategies to enable "parallelization across the method" for spectral deferred corrections (SDC). Using standard low-order time-stepping methods in an iterative fashion, SDC can be seen as preconditioned Picard…

Numerical Analysis · Mathematics 2017-03-24 Robert Speck

In this paper, we present a new SDC scheme for solving semi-explicit DAEs with the ability to be parallelized in which only the differential equations are numerically integrated is presented. In Shu et al. (2007) it was shown that SDC for…

Numerical Analysis · Mathematics 2026-01-26 Matthias Bolten , Lisa Wimmer

This paper presents a semi-implicit spectral deferred correction (SDC) method for incompressible Navier-Stokes problems with variable viscosity and time-dependent boundary conditions. The proposed method integrates elements of velocity- and…

Numerical Analysis · Mathematics 2020-10-28 Jörg Stiller

We present an arbitrarily high-order, conditionally stable, partitioned spectral deferred correction (SDC) method for solving multiphysics problems using a sequence of pre-existing single-physics solvers. This method extends the work in [1,…

Numerical Analysis · Mathematics 2020-04-07 Daniel Z. Huang , Will Pazner , Per-Olof Persson , Matthew J. Zahr

Semi-implicit spectral deferred correction (SDC) methods provide a systematic approach to construct time integration methods of arbitrarily high order for nonlinear evolution equations including conservation laws. They converge towards $A$-…

Numerical Analysis · Mathematics 2025-01-29 Joerg Stiller

Parallel-across-the method time integration can provide small scale parallelism when solving initial value problems. Spectral deferred corrections (SDC) with a diagonal sweeper, which is closely related to iterated Runge-Kutta methods…

Numerical Analysis · Mathematics 2025-02-12 Gayatri Čaklović , Thibaut Lunet , Sebastian Götschel , Daniel Ruprecht

In this paper, we develop a low-rank method with high-order temporal accuracy using spectral deferred correction (SDC) to compute linear matrix differential equations. In [1], a low rank numerical method is proposed to correct the modeling…

Numerical Analysis · Mathematics 2024-12-13 Shun Li , Yan Jiang , Yingda Cheng

We present an adaptive arbitrary-order accurate time-stepping numerical scheme for the flow of vesicles suspended in Stokesian fluids. Our scheme can be summarized as an approximate implicit spectral deferred correction (SDC) method.…

Numerical Analysis · Mathematics 2014-05-27 Bryan Quaife , George Biros

Integral deferred correction (IDC) methods have been shown to be an efficient way to achieve arbitrary high order accuracy and possess good stability properties. In this paper, we construct high order operator splitting schemes using the…

Numerical Analysis · Mathematics 2015-05-20 Andrew J. Christlieb , Yuan Liu , Zhengfu Xu

The spectral deferred correction method is a variant of the deferred correction method for solving ordinary differential equations. A benefit of this method is that is uses low order schemes iteratively to produce a high order…

Numerical Analysis · Mathematics 2020-07-07 Jehanzeb H. Chaudhry , J. B. Collins

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 complex chemistry. Our strategy employs parallelization across…

Numerical Analysis · Mathematics 2018-10-03 Francois Hamon , Marcus Day , Michael Minion

An alternative first step approximation based on subgrid artificial viscosity modeling (SAV) is proposed for defect-deferred correction method (DDC) for incompresible Navier-Stokes equation at high Reynolds number. This new approach not…

Numerical Analysis · Mathematics 2020-06-02 Mustafa Aggul

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 on a multi-implicit spectral deferred correction (MISDC)…

Numerical Analysis · Mathematics 2016-08-24 Will Pazner , Andrew Nonaka , John Bell , Marcus Day , Michael Minion

The main goal of this paper is to investigate the order reduction phenomenon that appears in the integral deferred correction (InDC) methods based on implicit-explicit (IMEX) Runge-Kutta (R-K) schemes when applied to a class of stiff…

Numerical Analysis · Mathematics 2017-01-18 S. Boscarino , J. Qiu , G. Russo
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