Related papers: Review and Recent Developments on the Perfectly Ma…
A nonlinear Helmholtz equation (NLH) with high wave number and Sommerfeld radiation condition is approximated by the perfectly matched layer (PML) technique and then discretized by the linear finite element method (FEM).…
Simulating the propagation of elastic waves in multi-layered media has many applications. A common approach is to use matrix methods where the elastic wave-field within each material layer is represented by a sum of partial-waves along with…
When the electromagnetic wave is incident on the periodic structures, in addition to the scattering field, some guided modes that are traveling in the periodic medium could be generated. In the present paper, we study the calculation of…
We analyse the convergence of numerical schemes in the GDM-ELLAM (Gradient Discretisation Method-Eulerian Lagrangian Localised Adjoint Method) framework for a strongly coupled elliptic-parabolic PDE which models miscible displacement in…
The convergence rate of domain decomposition methods (DDMs) strongly depends on the transmission condition at the interfaces between subdomains. Thus, an important aspect in improving the efficiency of such solvers is careful design of…
Multimodal Large Language Models (MLLMs) have achieved success across various domains. However, their applicability tends to degrade when confronted with different types of data inputs, especially for MLLMs that have been fine-tuned for…
For numerical simulations of highly relativistic and transversely accelerated charged particles including radiation fast algorithms are needed. While the radiation in particle accelerators has wavelengths in the order of 100 um the…
The perfectly matched layers (PML) and exterior complex scaling (ECS) methods for absorbing boundary conditions are analyzed using spectral decomposition. Both methods are derived through analytical continuations from unitary to contractive…
Flows in which the primary features of interest do not rely on high-frequency acoustic effects, but in which long-wavelength acoustics play a nontrivial role, present a computational challenge. Integrating the entire domain with…
We analyse wave propagation in two-dimensional bianisotropic media with the Finite Element Method (FEM). We start from the Maxwell-Tellegen's equations in bianisotropic media, and derive some system of coupled Partial Difference Equations…
We present an efficient nodal discontinuous Galerkin method for approximating nearly incompressible flows using the Boltzmann equations. The equations are discretized with Hermite polynomials in velocity space yielding a first order…
We study and implement a simple method, based on the Perfectly Matched Layer approach, to treat non reflecting boundary conditions with the Smoothed Particles Hydrodynamics numerical algorithm. The method is based on the concept of physical…
In this work we study the dynamic behaviour of compound shells of revolution partially filled with an ideal incompressible fluid based on boundary-value problems. New analytical mathematical model with corresponding discrete scheme for the…
The Krylov subspace projection approach is a well-established tool for the reduced order modeling of dynamical systems in the time domain. In this paper, we address the main issues obstructing the application of this powerful approach to…
An FFT-based algorithm is developed to simulate the propagation of elastic waves in heterogeneous $d$-dimensional rectangular shape domains. The method allows one to prescribe the displacement as a function of time in a subregion of the…
We consider a wide variety of scattering problems including scattering by Dirichlet, Neumann, and penetrable obstacles. We consider a radial perfectly-matched layer (PML) and show that for any PML width and a steep-enough scaling angle, the…
Multiscale problems are computationally costly to solve by direct simulation because the smallest scales must be represented over a domain determined by the largest scales of the problem. We have developed and analyzed new numerical methods…
In this paper, we investigate the use of a mass lumped fully explicit time stepping scheme for the discretisation of the wave equation with underlying material parameters that vary at arbitrarily fine scales. We combine the leapfrog scheme…
A new construction of an absorbing boundary condition for indefinite Helmholtz problems on unbounded domains is presented. This construction is based on a near-best uniform rational interpolant of the inverse square root function on the…
An algorithm for a family of self-starting high-order implicit time integration schemes with controllable numerical dissipation is proposed for both linear and nonlinear transient problems. This work builds on the previous works of the…