3 citations · 9 across the 15 of their papers we have counts for
15 papers
New error estimates of the weighted projections
Qiya Hu, Yuhan Luo
It is known that the weighted projection operator exhibits approximation properties different from those of the classical projection, in the sense that the error…
An unconditionally convergent discontinuous Galerkin neural network method activated by plane waves for Helmholtz equation and Maxwell's equations
Long Yuan, Menghui Wu, Qiya Hu +1
In this paper we propose a discontinuous Galerkin plane wave neural network (DGPWNN) method for approximately solving Helmholtz equation and Maxwell's equations. In this method, we…
A novel coarse space applying to the weighted Schwarz method for Helmholtz equations
Qiya Hu, Ziyi Li
In this paper we are concerned with restricted additive Schwarz with local impedance transformation conditions for a family of Helmholtz problems in two dimensions. These problems…
A discontinuous plane wave neural network method for Helmholtz equation and time-harmonic Maxwell's equations
Long Yuan, Qiya Hu
In this paper we propose a {\it discontinuous} plane wave neural network (DPWNN) method with refinement for approximately solving Helmholtz equation and time-harmonic Maxwell…
A plane wave method based on approximate wave directions for two dimensional Helmholtz equations with large wave numbers
Qiya Hu, Zezhong Wang
In this paper we present and analyse a high accuracy method for computing wave directions defined in the geometrical optics ansatz of Helmholtz equation with variable wave number.…
A geometric optics ansatz-based plane wave method for two dimensional Helmholtz equations with variable wave numbers
Qiya Hu, Zezhong Wang
In this paper we develop a plane wave type method for discretization of homogeneous Helmholtz equations with variable wave numbers. In the proposed method, local basis functions (o…
Plane Wave Discontinuous Galerkin methods for the Helmholtz equation and Maxwell equations in Anisotropic Media
Long Yuan, Qiya Hu
In this paper we are concerned with plane wave discontinuous Galerkin (PWDG) methods for Helmholtz equation and time-harmonic Maxwell equations in three-dimensional anisotropic med…
A novel least squares method for Helmholtz equations with large wave numbers
Qiya Hu, Rongrong Song
In this paper we are concerned with numerical methods for nonhomogeneous Helmholtz equations in inhomogeneous media. We design a least squares method for discretization of the cons…
A substructuring preconditioner with vertex-related interface solvers for elliptic-type equations in three dimensions
Qiya Hu, Shaoliang Hu
In this paper we propose a variant of the substructuring preconditioner for solving three-dimensional elliptic-type equations with strongly discontinuous coefficients. In the propo…
A variant of the plane wave least squares method for the time-harmonic Maxwell's equations
Qiya Hu, Rongrong Song
In this paper we are concerned with the plane wave method for the discretization of time-harmonic Maxwell's equations in three dimensions. As pointed out in [6], it is difficult to…
Convergence of HX Preconditioner for Maxwell's Equations with Jump Coefficients (ii): The Main Results
Qiya Hu
This paper is the second one of two serial articles, whose goal is to prove convergence of HX Preconditioner (proposed by Hiptmair and Xu, 2007) for Maxwell's equations with jump c…
Convergence of HX Preconditioner for Maxwell's Equations with Jump Coefficients (i): Various Extensions of The Regular Helmholtz Decomposition
Qiya Hu
This paper is the first one of two serial articles, whose goal is to prove convergence of HX Preconditioner (proposed by Hiptmair and Xu 2007) for Maxwell's equations with jump coe…
Substructuring preconditioners with novel interface solvers for general elliptic-type equations in three dimensions
Qiya Hu, Shaoliang Hu
In this paper we propose two variants of the substructuring preconditioner for solving three-dimensional elliptic-type equations with strongly discontinuous coefficients. In the ne…
Novel multilevel preconditioners for the systems arising from plane wave discretization of Helmholtz equations with large wave numbers
Qiya Hu, Xuan Li
In this paper we are concerned with fast algorithms for the systems arising from the plane wave discretizations for two-dimensional Helmholtz equations with large wave numbers. We…
A Nonconforming Finite Element Method for Fourth Order Curl Equations in R^3
Bin Zheng, Qiya Hu, Jinchao Xu
In this paper we present a nonconforming finite element method for solving fourth order curl equations in three dimensions arising from magnetohydrodynamics models. We show that th…