Related papers: An Efficient Finite Difference-based Implicit Solv…
Several methods exist for finding ground (as well as excited) states of nonlinear waves equations. In this paper we first introduce two modifications of the so-called accelerated imaginary-time evolution method (AITEM). In our first…
It remains an open problem to find the optimal configuration of phase shifts under the discrete constraint for intelligent reflecting surface (IRS) in polynomial time. The above problem is widely believed to be difficult because it is not…
A finite difference numerical method is investigated for fractional order diffusion problems in one space dimension. For this, a mathematical model is developed to incorporate homogeneous Dirichlet and Neumann type boundary conditions. The…
Currently existing energy-stable parametric finite element methods for surface diffusion flow and other flows are usually limited to first-order accuracy in time. Designing a high-order algorithm for geometric flows that can also be…
We explore the use of field solvers as approximations of classical Vlasov-Poisson systems. This correspondence is investigated in both electrostatic and gravitational contexts. We demonstrate the ability of field solvers to be excellent…
Phase-field models are widely employed to simulate microstructure evolution during processes such as solidification or heat treatment. The resulting partial differential equations, often strongly coupled together, may be solved by a broad…
The spatial discretization of the magnetic vector potential formulation of magnetoquasistatic field problems results in an infinitely stiff differential-algebraic equation system. It is transformed into a finitely stiff ordinary…
Recently, electromagnetic surrogate solvers, trained on solutions of Maxwell's equations under specific simulation conditions, enabled fast inference of computationally expensive simulations. However, conventional electromagnetic surrogate…
In this paper, we construct efficient schemes based on the scalar auxiliary variable (SAV) block-centered finite difference method for the modified phase field crystal (MPFC) equation, which is a sixth-order nonlinear damped wave equation.…
In this paper we consider the numerical approximation of the incompressible surface Navier--Stokes equations on an evolving surface. For the discrete representation of the moving surface we use parametric finite elements of degree $\ell…
The novel contribution of this paper relies in the proposal of a fully implicit numerical method designed for nonlinear degenerate parabolic equations, in its convergence/stability analysis, and in the study of the related computational…
The phase field crystal (PFC) method is an efficient technique for simulating the evolution of crystalline microstructures at atomistic length scales and diffusive time scales. Due to the high-order derivatives (sixth-order) and the…
In this investigation we revisit the concept of "effective free surfaces" arising in the solution of the time-averaged fluid dynamics equations in the presence of free boundaries. This work is motivated by applications of the optimization…
A numerical explicit method to evaluates transient solutions of linear partial differential inhomogeneous equation with constant coefficients is proposed. A general form of the scheme for a specific linear inhomogeneous equation is shown.…
Electromagnetic metasurfaces offer the capability to realize almost arbitrary power conserving field transformations. These field transformations are governed by the generalized sheet transition conditions, which relate the tangential…
In this paper we investigate a sub-diffusion equation for simulating the anomalous diffusion phenomenon in real physical environment. Based on an equivalent transformation of the original sub-diffusion equation followed by the use of a…
Surface integral equation (SIE) methods are of great interest for the numerical solution of Maxwell's equations in the presence of homogeneous objects. However, existing SIE algorithms have limitations, either in terms of scalability,…
A class of abstract nonlinear time-periodic evolution problems is considered which arise in electrical engineering and other scientific disciplines. An efficient solver is proposed for the systems arising after discretization in time based…
We propose and analyse a novel surface finite element method that preserves the invariant regions of systems of semilinear parabolic equations on closed compact surfaces in $\mathbb{R}^3$ under discretisation. We also provide a…
Model reduction methods often aim at an identification of slow invariant manifolds in the state space of dynamical systems modeled by ordinary differential equations. We present a predictor corrector method for a fast solution of an…