Gautschi-type and implicit-explicit integrators for constrained wave equations

2025/05/28 by Altmann, R., Dörich, B., Zimmer, C.
#FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2505.22532

Abstract

This paper deals with the construction and analysis of two integrators for (semi-linear) second-order partial differential-algebraic equations of semi-explicit type. More precisely, we consider an implicit-explicit Crank-Nicolson scheme as well as an exponential integrator of Gautschi type. For this, well-known wave integrators for unconstrained systems are combined with techniques known from the field of differential-algebraic equations. This results in efficient time stepping schemes that are provable of second order. Moreover, we discuss the practical implementation of the Gautschi-type method, which involves the solution of certain saddle point problems. The theoretical results are verified by a numerical experiment for the wave equation with kinetic boundary conditions.

Citations

• Speeding up Krylov subspace methods for computing f(A)b via randomization
• Splitting schemes for the semi-linear wave equation with dynamic boundary conditions
• Continuous Galerkin Schemes for Semi-Explicit Differential-Algebraic Equations
• Exponential integrators for semi-linear parabolic problems with linear constraints
• Finite element error analysis of wave equations with dynamic boundary\n conditions: L² estimates
• A PDAE formulation of parabolic problems with dynamic boundary\n conditions
• Discontinuous Galerkin Time Discretization Methods for Parabolic\n Problems with Linear Constraints
• Implicit-Explicit Methods for Time-Dependent Partial Differential Equations
• Numerical integration of ordinary differential equations based on trigonometric polynomials

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• Numerical treatment of interfaces for second-order wave equations