相关论文: IMEX Runge-Kutta Parareal for Non-Diffusive Equati…

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. These time discretizations preserve the monotonicity…

We discuss Implicit-Explicit (IMEX) Runge Kutta methods which are particularly adapted to stiff kinetic equations of Boltzmann type. We consider both the case of easy invertible collision operators and the challenging case of Boltzmann…

In this paper, we present a method that enables solving in parallel the Euler-Lagrange system associated with the optimal control of a parabolic equation. Our approach is based on an iterative update of a sequence of intermediate targets…

This paper proposes a framework to assess the stability of an ordinary differential equation which is coupled to a 1D-partial differential equation (PDE). The stability theorem is based on a new result on Integral Quadratic Constraints…

The nonhydrostatic High Order Method Modeling Environment (HOMME-NH) atmospheric dynamical core supports acoustic waves that propagate significantly faster than the advective wind speed, thus greatly limiting the timestep size that can be…

A novel optimization procedure for the generation of stability polynomials of stabilized explicit Runge-Kutta methods is devised. Intended for semidiscretizations of hyperbolic partial differential equations, the herein developed approach…

High order spatial discretizations with monotonicity properties are often desirable for the solution of hyperbolic PDEs. These methods can advantageously be coupled with high order strong stability preserving time discretizations. The…

We present second-order optimally stable Implicit-Explicit (IMEX) Runge-Kutta (RK) schemes with application to a modified set of shallow water equations that can be used to model the dynamics of lava flows. The schemes are optimally stable…

A new parallel-in-time iterative method is proposed for solving the homogeneous second-order wave equation. The new method involves a coarse scale propagator, allowing for larger time steps, and a fine scale propagator which fully resolves…

We consider high order, implicit Runge-Kutta schemes to solve time-dependent stiff PDEs on dynamically adapted grids generated by multiresolution analysis for unsteady problems disclosing localized fronts. The multiresolution finite volume…

Exponential time differencing methods is a power tool for high-performance numerical simulation of computationally challenging problems in condensed matter physics, fluid dynamics, chemical and biological physics, where mathematical models…

Fractional-step methods are a popular and powerful divide-and-conquer approach for the numerical solution of differential equations. When the integrators of the fractional steps are Runge--Kutta methods, such methods can be written as…

This paper deals with stability of classical Runge-Kutta collocation methods. When such methods are embedded in linearly implicit methods as developed in [12] and used in [13] for the time integration of nonlinear evolution PDEs, the…

The parareal algorithm represents an important class of parallel-in-time algorithms for solving evolution equations and has been widely applied in practice. To achieve effective speedup, the choice of the coarse propagator in the algorithm…

Discrete variational methods show excellent performance in numerical simulations of different mechanical systems. In this paper, we introduce an iterative procedure for the solution of discrete variational equations for boundary value…

This work focuses on the development of a new class of high-order accurate methods for multirate time integration of systems of ordinary differential equations. Unlike other recent work in this area, the proposed methods support mixed…

Finite differences and Runge-Kutta time stepping schemes used in Computational AeroAcoustics simulations are often optimized for low dispersion and dissipation (e.g. DRP or LDDRK schemes) when applied to linear problems in order to…

With this short note, we close a gap in the linear stability theory of block predictor-corrector Runge-Kutta schemes originally proposed for the parallel solution of ODEs.

We present novel entropy-conservative and entropy-stable multirate Runge-Kutta methods based on Paired Explicit Runge-Kutta (P-ERK) schemes with relaxation for conservation laws and related systems of partial differential equations.…

We consider a PDE-constrained optimization problem of tracking type with parabolic state equation. The solution to the problem is characterized by the Karush-Kuhn-Tucker (KKT) system, which we formulate using a strong variational…