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Simulating physical problems involving multi-time scale coupling is challenging due to the need of solving these multi-time scale processes simultaneously. In response to this challenge, this paper proposed an explicit multi-time step…
This paper is concerned with the time-step condition of commonly-used linearized semi-implicit schemes for nonlinear parabolic PDEs with Galerkin finite element approximations. In particular, we study the time-dependent nonlinear Joule…
A new iterative technique is presented for solving of initial value problem for certain classes of multidimensional linear and nonlinear partial differential equations. Proposed iterative scheme does not require any discretization,…
We analyze the convergence rates to a planar interface in the Mullins-Sekerka model by applying a relaxation method based on relationships among distance, energy, and dissipation. The relaxation method was developed by two of the authors in…
Time delays are ubiquitous in industrial processes, and they must be accounted for when designing control algorithms because they have a significant effect on the process dynamics. Therefore, in this work, we propose a simultaneous approach…
We present and analyze a new space-time parallel multigrid method for parabolic equations. The method is based on arbitrarily high order discontinuous Galerkin discretizations in time, and a finite element discretization in space. The key…
We propose and analyze a second-order partitioned time-stepping method for a two-phase flow problem in porous media. The algorithm is based on a refactorization of Cauchy's one-leg $\theta$-method. The main part consists of the implicit…
Numerical schemes for the solution of the Euler equations have recently been developed, which involve the discretisation of the internal energy equation, with corrective terms to ensure the correct capture of shocks, and, more generally,…
We study efficient simulation of steady state for rarefied gas flow, which is modeled by the Boltzmann equation with BGK-type collision term. A nonlinear multigrid solver is proposed to resolve the efficiency issue by the following…
A coupling approach is presented to combine a wave-based method to the standard finite element method. This coupling methodology is presented here for the Helmholtz equation but it can be applied to a wide range of wave propagation…
Within this paper, we introduce partially and fully decoupled time stepping schemes for linear thermo-poroelasticity. This means that the mechanics, heat, and flow equations can be solved sequentially. We provide sufficient conditions on…
Asking for the optimal protocol of an external control parameter that minimizes the mean work required to drive a nano-scale system from one equilibrium state to another in finite time, Schmiedl and Seifert ({\it Phys. Rev. Lett.} {\bf 98},…
Constrained mechanical multibody systems arise in many important applications like robotics, vehicle and machinery dynamics and biomechanics of locomotion of humans. These systems are described by the Euler-Lagrange equations which are…
Problems with localized nonhomogeneous material properties present well-known challenges for numerical simulations. In particular, such problems may feature large differences in length scales, causing difficulties with meshing and…
In this paper, we consider the classical wave equation with time-dependent, spatially multiscale coefficients. We propose a fully discrete computational multiscale method in the spirit of the localized orthogonal decomposition in space with…
This paper is concerned with the optimized Schwarz waveform relaxation method and Ventcel transmission conditions for the linear advection-diffusion equation. A mixed formulation is considered in which the flux variable represents both…
We present a novel method for mixed-integer optimization problems with multivariate and Lipschitz continuous nonlinearities. In particular, we do not assume that the nonlinear constraints are explicitly given but that we can only evaluate…
In this article we present a parallel algorithm for simulation of the heat conduction process inside the so-called pulse cryogenic cell. This simulation is important for designing the device for portion injection of working gases into…
We introduce an Eulerian approach for problems involving one or more soft solids immersed in a fluid, which permits mechanical interactions between all phases. The reference map variable is exploited to simulate finite-deformation…
The two-scale computational homogenization method is proposed for modelling of locally periodic fluid-saturated media subjected a to large deformation induced by quasistatic loading. The periodic heterogeneities are relevant to the…