An efficient spectral‐Galerkin method based on a dimension reduction scheme for eigenvalue problems of Schrödinger equations
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DOI: 10.1002/mma.5500
Abstract: In this paper, we propose an efficient spectral‐Galerkin method based on a dimension reduction scheme for eigenvalue problems of Schrödinger equations. Firstly, we carry out a truncation from a three‐dimensional unbounded domain to a bounded… read more here.
Keywords: eigenvalue; method; spectral galerkin; efficient spectral ... See more keywords
A stable discontinuous Galerkin method for the perfectly matched layer for elastodynamics in first order form
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DOI: 10.1007/s00211-020-01160-w
Abstract: We present a stable discontinuous Galerkin (DG) method with a perfectly matched layer (PML) for three and two space dimensional linear elastodynamics, in velocity-stress formulation, subject to well-posed linear boundary conditions. First, we consider the… read more here.
Keywords: stable discontinuous; energy; discontinuous galerkin; method ... See more keywords
Developing three-dimensional mesh-free Galerkin method for structural analysis of general polygonal geometries
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DOI: 10.1007/s00366-019-00749-6
Abstract: In this paper, triangular prismatic cells for background integration on mesh-free methods are introduced and the Gauss integration scheme is developed in these cells. The cells are used in the mesh-free Galerkin method for free vibration, static and… read more here.
Keywords: free galerkin; analysis general; general polygonal; analysis ... See more keywords
A POD reduced-order model based on spectral Galerkin method for solving the space-fractional Gray–Scott model with error estimate
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DOI: 10.1007/s00366-020-01195-5
Abstract: This paper deals with developing a fast and robust numerical formulation to simulate a system of fractional PDEs. At the first stage, the time variable is approximated by a finite difference method with first-order accuracy.… read more here.
Keywords: reduced order; order; method; model ... See more keywords
A fully discrete Galerkin method for Abel-type integral equations
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DOI: 10.1007/s10444-018-9598-4
Abstract: In this paper, we present a Galerkin method for Abel-type integral equation with a general class of kernel. Stability and quasi-optimal convergence estimates are derived in fractional-order Sobolev norms. The fully-discrete Galerkin method is defined… read more here.
Keywords: type integral; abel type; method abel; method ... See more keywords
An Adaptive SDG Method for the Stokes System
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DOI: 10.1007/s10915-016-0265-y
Abstract: Staggered grid techniques are attractive ideas for flow problems due to their more enhanced conservation properties. Recently, a staggered discontinuous Galerkin method is developed for the Stokes system. This method has several distinctive advantages, namely… read more here.
Keywords: discontinuous galerkin; method; staggered discontinuous; galerkin method ... See more keywords
The Discrete Stochastic Galerkin Method for Hyperbolic Equations with Non-smooth and Random Coefficients
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DOI: 10.1007/s10915-017-0426-7
Abstract: We develop a general polynomial chaos (gPC) based stochastic Galerkin (SG) for hyperbolic equations with random and singular coefficients. Due to the singular nature of the solution, the standard gPC-SG methods may suffer from a… read more here.
Keywords: method hyperbolic; hyperbolic equations; discrete stochastic; stochastic galerkin ... See more keywords
A Robust Numerical Method for the Random Interface Grating Problem via Shape Calculus, Weak Galerkin Method, and Low-Rank Approximation
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DOI: 10.1007/s10915-018-0712-z
Abstract: We present an efficient numerical algorithm to solve random interface grating problems based on a combination of shape derivatives, the weak Galerkin method, and a low-rank approximation technique. By using the asymptotic perturbation approach via… read more here.
Keywords: method; weak galerkin; rank approximation; low rank ... See more keywords
Cross validation of discontinuous Galerkin method and Monte Carlo simulations of charge transport in graphene on substrate
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DOI: 10.1007/s11587-016-0298-4
Abstract: The aim of this work is to simulate the charge transport in a monolayer graphene on a substrate. This requires the inclusion of the scatterings of the charge carriers with the impurities and the phonons… read more here.
Keywords: charge transport; discontinuous galerkin; graphene; monte carlo ... See more keywords
A Trefftz-discontinuous Galerkin method for time-harmonic elastic wave problems
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DOI: 10.1007/s40314-019-0900-y
Abstract: In this paper, we develop a plane wave discontinuous Galerkin method combined with local spectral element method for the elastic wave propagation in two and three space dimensions. We derive the error estimates of the… read more here.
Keywords: elastic wave; discontinuous galerkin; method time; trefftz discontinuous ... See more keywords
Exponential Jacobi-Galerkin method and its applications to multidimensional problems in unbounded domains
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DOI: 10.1016/j.apnum.2020.05.017
Abstract: Abstract Modeling an infinite domain arises while simulating physical applications frequently. It is like attempting to model the effects and properties of the ocean in a bucket. In this paper, we develop a spectral Galerkin… read more here.
Keywords: exponential jacobi; unbounded domains; galerkin method;