相关论文: A High-Order Ultra-Weak Variational Formulation fo…
Common trends in model order reduction of large nonlinear finite-element-discretized systems involve the introduction of a linear mapping into a reduced set of unknowns, followed by Galerkin projection of the governing equations onto a…
Plane-wave Trefftz methods (PWB) for the Helmholtz equation offer significant advantages over standard discretization approaches whose implementation employs more general polynomial basis functions. A disadvantage of these methods is the…
The Unified Gas-Kinetic Wave-Particle (UGKWP) method, developed for multiscale simulation of partially ionized plasmas, has been extended to unstructured meshes, enabling the modeling of electromagnetic flows around a hemisphere across…
We propose a high-order discontinuous Galerkin scheme for nonlinear acoustic waves on polytopic meshes. To model sound propagation with and without losses, we use Westervelt's nonlinear wave equation with and without strong damping.…
The focus of this article is on shape and topology optimization of transient vibroacoustic problems. The main contribution is a transient problem formulation that enables optimization over wide ranges of frequencies with complex signals,…
In this work, we develop variational formulations of Petrov-Galerkin type for one-dimensional fractional boundary value problems involving either a Riemann-Liouville or Caputo derivative of order $\alpha\in(3/2, 2)$ in the leading term and…
A systematic numerical study on weak Galerkin (WG) finite element method for second order linear parabolic problems is presented by allowing polynomial approximations with various degrees for each local element. Convergence of both…
This paper develops a weak Galerkin (WG) finite element method of arbitrary order for the steady incompressible Magnetohydrodynamics equations. The WG scheme uses piecewise polynomials of degrees $k(k\geq 1),k,k-1$, and $k-1$ respectively…
Metasurfaces, consisting of large arrays of interacting subwavelength scatterers, pose significant challenges for general-purpose computational methods due to their large electric dimensions and multiscale nature. This paper introduces an…
High-order methods offer superior dispersion and dissipation properties compared to low-order schemes but require robust stabilization for discontinuities. To ensure stability, local artificial viscosity is common, but often degrades…
We develop a sparse multiscale operator-adapted wavelet decomposition-based finite element method (FEM) on unstructured polygonal mesh hierarchies obtained via a coarsening procedure. Our approach decouples different resolution levels,…
In many time-harmonic electromagnetic wave problems, the considered geometry exhibits an axial symmetry. In this case, by exploiting a Fourier expansion along the azimuthal direction, fully three-dimensional (3D) calculations can be carried…
In this paper a hybridized weak Galerkin (HWG) finite element method for solving the Stokes equations in the primary velocity-pressure formulation is introduced. The WG method uses weak functions and their weak derivatives which are defined…
An adaptive finite element method is presented for the elastic scattering of a time-harmonic plane wave by a periodic surface. First, the unbounded physical domain is truncated into a bounded computational domain by introducing the…
To strike a balance between modeling accuracy and computational efficiency for simulations of ultrasound waves in soft tissues, we derive a pseudodifferential factorization of the wave operator with fractional attenuation. This…
We propose a generalized finite element method for the strongly damped wave equation with highly varying coefficients. The proposed method is based on the localized orthogonal decomposition introduced and is designed to handle independent…
We introduce and rigorously analyze a least-squares weak Galerkin (LS-WG) finite element method for the severely ill-posed Cauchy problem of convection--diffusion equations. The proposed framework utilizes weak derivatives defined on a…
In this paper, we define new unfitted finite element methods for numerically approximating the solution of surface partial differential equations using bulk finite elements. The key idea is that the $n$-dimensional hypersurface, $\Gamma…
Two methods are explained to exactly solve Maxwell's equations where permittivity, permeability and conductivity may vary in space. In the constitutive relations, retardation is regarded. If the material properties depend but on one…
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).…