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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
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…