相关论文: An hp-Adaptive Sampling Algorithm on Dispersion Re…
In this work we investigate the computation of dispersion relation (i.e., band functions) for three-dimensional photonic crystals, formulated as a parameterized Maxwell eigenvalue problem, using a novel hp-adaptive sampling algorithm. We…
The numerical approximation of solutions of parametric or stochastic hyperbolic PDEs is still a serious challenge. Because of shock singularities, most methods from the elliptic and parabolic regime, such as reduced basis methods, POD or…
Dispersion relation reflects the dependence of wave frequency on its wave vector when the wave passes through certain material. It demonstrates the properties of this material and thus it is critical. However, dispersion relation…
We analyze an adaptive boundary element method for the weakly-singular and hypersingular integral equations for the 2D and 3D Helmholtz problem. The proposed adaptive algorithm is steered by a residual error estimator and does not rely on…
To avoid ineffective collisions between the equilibrium states, the hybrid method with deviational particles (HDP) has been proposed to integrate the Vlasov-Poisson-Landau system, while leaving a new issue in sampling deviational particles…
Numerical calculation of modes in dispersive and absorptive systems is performed using the finite element method. The dispersion is tackled in the frame of an extension of Maxwell's equations where auxiliary fields are added to the…
In this article we develop an $hp$-adaptive refinement procedure for Trefftz discontinuous Galerkin methods applied to the homogeneous Helmholtz problem. Our approach combines not only mesh subdivision (h-refinement) and local basis…
When a numerical simulation has to handle a physics problem with a wide range of time-dependent length scales, dynamically adaptive discretizations can be the method of choice. We present a major upgrade to the numerical relativity code…
An adaptive algorithm for computing eigenmodes and propagation constants of optical fibers is proposed. The algorithm is built using a dual-weighted residual error estimator. The residuals are based on the eigensystem for leaky hybrid modes…
We introduce an adaptive finite element scheme for the efficient approximation of a (large) collection of eigenpairs of selfadjoint elliptic operators in which the adaptive refinement is driven by the solution of a single source problem --…
We implement an adaptive mesh algorithm for calculating the space and time dependence of the atomic density field during materials processing. Our numerical approach uses the systematic renormalization-group formulation of the phase field…
This paper presents an $hp$ a posteriori error analysis for the 2D Helmholtz equation that is robust in the polynomial degree $p$ and the wave number $k$. For the discretization, we consider a discontinuous Galerkin formulation that is…
We consider PDE eigenvalue problems as they occur in two-dimensional photonic crystal modeling. If the permittivity of the material is frequency-dependent, then the eigenvalue problem becomes nonlinear. In the lossless case, linearization…
Panel-based, kernel-split quadrature is currently one of the most efficient methods available for accurate evaluation of singular and nearly singular layer potentials in two dimensions. However, it can fail completely for the layer…
It is well known that the quasi-optimality of the Galerkin finite element method for the Helmholtz equation is dependent on the mesh size and the wave-number. In the literature, different criteria have been proposed to ensure uniform…
The calculation of potential energy surfaces for quantum dynamics can be a time consuming task -- especially when a high level of theory for the electronic structure calculation is required. We propose an adaptive interpolation algorithm…
This article is concerned with the numerical solution of convex variational problems. More precisely, we develop an iterative minimisation technique which allows for the successive enrichment of an underlying discrete approximation space in…
In this paper a new hp-adaptive strategy for elliptic problems based on refinement history is proposed, which chooses h-, p- or hp-refinement on individual elements according to a posteriori error estimate, as well as smoothness estimate of…
Panel-based, kernel-split quadrature is currently one of the most efficient methods available for accurate evaluation of singular and nearly singular layer potentials in two dimensions. However, it can fail completely for the layer…
A new domain decomposition method is introduced for the heterogeneous 2-D and 3-D Helmholtz equations. Transmission conditions based on the perfectly matched layer (PML) are derived that avoid artificial reflections and match incoming and…