Related papers: Improving the IMEX method with a residual balanced…
The choice of numerical integrator in approximating solutions to dynamic partial differential equations depends on the smallest time-scale of the problem at hand. Large-scale deformations in elastic solids contain both shear waves and bulk…
A non-uniform implicit-explicit L1 mixed finite element method (IMEX-L1-MFEM) is investigated for a class of time-fractional partial integro-differential equations (PIDEs) with space-time dependent coefficients and non-self-adjoint elliptic…
Neural PDE solvers offer a powerful tool for modeling complex dynamical systems, but often struggle with error accumulation over long time horizons and maintaining stability and physical consistency. We introduce a multiscale implicit…
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…
In two preceding papers we have shown that, when reaction networks are well-removed from equilibrium, explicit asymptotic and quasi-steady-state approximations can give algebraically-stabilized integration schemes that rival standard…
We propose an efficient, accurate and robust IMEX solver for the compressible Navier-Stokes equation describing non-ideal gases with general equations of state. The method, which is based on an $h-$adaptive Discontinuos Galerkin spatial…
To integrate large systems of nonlinear differential equations in time, we consider a variant of nonlinear waveform relaxation (also known as dynamic iteration or Picard-Lindel\"of iteration), where at each iteration a linear inhomogeneous…
We analyze the behaviour of an ensemble of time integrators applied to the semi-discrete problem resulting from the spectral discretization of the equations describing Boussinesq convection in a cylindrical annulus. The equations are cast…
We introduce a novel Multi-Order Monte Carlo approach for uncertainty quantification in the context of multiscale time-dependent partial differential equations. The new framework leverages Implicit-Explicit Runge-Kutta time integrators to…
This paper developed a method called "modified exponential cubic B-Spline differential quadrature (mExp-DQM) for space discretization together with a time integration algorithm" for the numerical computation of hyperbolic telegraph equation…
In recent decades, there have been many attempts to construct symplectic integrators with variable time steps, with rather disappointing results. In this paper we identify the causes for this lack of performance, and find that they fall…
We construct new higher-order implicit-explicit (IMEX) schemes using the generalized scalar auxiliary variable (GSAV) approach for the Landau-Lifshitz equation. These schemes are linear, length preserving and only require solving one…
One way of improving the behavior of finite element schemes for classical, time-dependent Maxwell's equations, is to render them from their hyperbolic character to elliptic form. This paper is devoted to the study of the stabilized linear…
The paper is concerned with the development of efficient and accurate solution procedures for the isogeometric boundary element method (BEM) when applied to problems that contain inclusions that have elastic properties different to the…
In recent years, the embedding approach for solving switched optimal control problems has been developed in a series of papers. However, the embedding approach, which advantageously converts the hybrid optimal control problem to a classical…
We present a new framework for the solution of mathematical programs with equilibrium constraints (MPECs). In this algorithmic framework, an MPECs is viewed as a concentration of an unconstrained optimization which minimizes the…
A method for enhancing the stability and robustness of explicit schemes in computational fluid dynamics is presented. The method is based in reformulating explicit schemes in matrix form, which cane modified gradually into semi or…
Minibatch decomposition methods for empirical risk minimization are commonly analysed in a stochastic approximation setting, also known as sampling with replacement. On the other hands modern implementations of such techniques are…
Railway Wireless Power Transfer (WPT) is a promising non-contact power supply solution, but constructing prototypes for controller testing can be both costly and unsafe. Real-time hardware-in-the-loop simulation is an effective and secure…
Rational exponential integrators (REXI) are a class of numerical methods that are well suited for the time integration of linear partial differential equations with imaginary eigenvalues. Since these methods can be parallelized in time (in…