We introduce vertex block descent, a block coordinate descent solution for the variational form of implicit Euler through vertex-level Gauss-Seidel iterations. It operates with local vertex position updates that achieve reductions in global variational ...

In recent years, the SUite of Nonlinear and DIfferential/ALgebraic equation Solvers (SUNDIALS) has been redesigned to better enable the use of application-specific and third-party algebraic solvers and data structures. Throughout this work, we have ...

We introduce a technique that makes every explicit Runge--Kutta (ERK) time stepping method invariant domain preserving and mass conservative when applied to high-order discretizations of the Cauchy problem associated with systems of nonlinear conservation ...

In this paper we consider the numerical solution of second-order semilinear differential equations for which the stiffness is induced by only a few components of the linear part. For such problems, the leapfrog scheme suffers from severe restrictions on the ...

In this paper we propose two exponential integrators of first and second order applied to a class of quasilinear wave-type equations. The analytical framework is an extension of the classical Kato framework and covers quasilinear Maxwell's equations in ...

Fully implicit Runge--Kutta (IRK) methods have many desirable accuracy and stability properties as time integration schemes, but high-order IRK methods are not commonly used in practice with large-scale numerical PDEs because of the difficulty of solving the ...

Time integration methods for solving initial value problems are an important component of many scientific and engineering simulations. Implicit time integrators are desirable for their stability properties, which significantly relax restrictions on timestep ...

Time-harmonic solutions to the wave equation can be computed in the frequency or in the time domain. In the frequency domain, one solves a discretized Helmholtz equation, while in the time domain, the periodic solutions to a discretized wave equation are ...

Physics-based simulation methods for deformable objects suffer limitations due to the conflicting requirements that are placed on them. The work horse semi-implicit (SI) backward Euler method is very stable and inexpensive, but it is also a blunt ...

Diagonal norm finite difference based time integration methods in summation-by-parts form are investigated. The second, fourth, and sixth order accurate discretizations are proven to have eigenvalues with strictly positive real parts. This leads to ...

For the numerical solution of parabolic problems with a linear diffusion term, linearly implicit time integrators are considered. To reduce the cost on the linear algebra level, an alternating direction implicit approach is applied (so-called AMF-W-methods)...

This paper is dedicated to the improvement of the efficiency of the leapfrog method for linear and semilinear second-order differential equations. In numerous situations the strict CFL condition of the leapfrog method is the main bottleneck that thwarts its ...

We present a methodology for constructing time integrators for solving systems of first-order ordinary differential equations by using interpolating polynomials. Our approach is to combine ideas from complex analysis and approximation theory to construct ...

The time integration of differential equations obtained by the space discretization via finite differences of evolution parabolic PDEs with mixed derivatives in the elliptic operator is considered (the method of lines approach). W-methods (Rosenbrock-type ...

We analyze the extension of summation-by-parts operators and weak boundary conditions for solving initial boundary value problems involving second derivatives in time. A wide formulation is obtained by first rewriting the problem on first order form. This ...

In this paper we consider the full discretization of linear Maxwell's equations on spatial grids which are locally refined. For such problems, explicit time integration schemes become inefficient because the smallest mesh width results in a strict CFL ...

We study pseudotransient continuation ($\Psi$tc) as a nonlinear solver for implicit discretizations of combustion problems with detailed chemical models. Detailed models produce extreme stiffness, nonlinearity, and a transient instability associated with ...

Strong stability preserving (SSP) methods are designed primarily for time integration of nonlinear hyperbolic PDEs, for which the permissible SSP step size varies from one step to the next. We develop the first SSP linear multistep methods (of order two and ...

We present a monolithic approach to large-deformation fluid-structure interaction (FSI) problems that allows for choosing fully implicit, single-step and single-stage time integration schemes in the structure and fluid field independently, and hence is ...