scholarly journals Solution of Exterior Quasilinear Problems Using Elliptical Arc Artificial Boundary

Mathematics ◽  
2021 ◽  
Vol 9 (14) ◽  
pp. 1598
Author(s):  
Yajun Chen ◽  
Qikui Du
Keyword(s):  
Finite Element Method ◽  
Boundary Condition ◽  
Numerical Experiments ◽  
Bounded Region ◽  
The Finite Element Method ◽  
Artificial Boundary ◽  
Artificial Boundary Condition ◽  
Artificial Boundary Conditions ◽  
Kirchhoff Transformation ◽  
Quasilinear Problems

In this paper, the method of artificial boundary conditions for exterior quasilinear problems in concave angle domains is investigated. Based on the Kirchhoff transformation, the exact quasiliner elliptical arc artificial boundary condition is derived. Using the approximate elliptical arc artificial boundary condition, the finite element method is formulated in a bounded region. The error estimates are obtained. The effectiveness of our method is showed by some numerical experiments.

The finite element method for solving the oblique derivative boundary value problems in geodesy

2020 ◽  
Author(s):  
Marek Macák ◽  
Zuzana Minarechová ◽  
Róbert Čunderlík ◽  
Karol Mikula
Keyword(s):  
Finite Element Method ◽  
Boundary Condition ◽  
Finite Element ◽  
Numerical Experiments ◽  
Boundary Value ◽  
Satellite Orbits ◽  
The Finite Element Method ◽  
Hexahedral Elements ◽  
Grid Points ◽  
Element Method

<p>We present a novel approach to the solution of the geodetic boundary value problem with an oblique derivative boundary condition by the finite element method. Namely, we propose and analyse a finite element approximation of a Laplace equation holding on a domain with an oblique derivative boundary condition given on a part of its boundary. The oblique vector in the boundary condition is split into one normal and two tangential components and derivatives in tangential directions are approximated as in the finite difference method. Then we apply the proposed numerical scheme to local gravity field modelling. For our two-dimensional testing numerical experiments, we use four nodes bilinear quadrilateral elements and for a three-dimensional problem, we use hexahedral elements with eight nodes. Practical numerical experiments are located in area of Slovakia that is given by grid points located on the Earth's surface with uniform spacing in horizontal directions. Heights of grid points are interpolated from the SRTM30PLUS topography model. An upper boundary is in the height of 240 km above a reference ellipsoid WGS84 corresponding to an average altitude of the GOCE satellite orbits. Obtained solutions are compared to DVRM05.</p>

Time-Domain Stability of Artificial Boundary Condition Coupled with Finite Element for Dynamic and Wave Problems in Unbounded Media

2019 ◽  
Vol 16 (04) ◽  
pp. 1850099 ◽  
Author(s):  
Mi Zhao ◽  
Huifang Li ◽  
Xiuli Du ◽  
Piguang Wang
Keyword(s):  
Boundary Condition ◽  
Finite Element ◽  
Time Domain ◽  
The Finite Element Method ◽  
Artificial Boundary ◽  
Artificial Boundary Condition ◽  
Unbounded Media ◽  
The Time Domain ◽  
Wave Problems ◽  
Domain Stability

The finite element modeling of the dynamic and wave problems in unbounded media requires an artificial boundary condition to simulate the truncated infinite domain. The Dirichlet-to-Neumann boundary condition has been transformed from frequency to time domain by using the rational function approximation and auxiliary variable technique. It is extended to three-dimensional layer problem here. The resulting artificial boundary condition is stable itself in time domain, whereas the time-domain instability of the artificial boundary condition coupled with the finite element method is found for the foundation vibration recently and for the wave propagation here. A simple and effective method that introduces the damping proportional to the stiffness matrix in the finite element method is given to cure such coupling instability completely. The stabilized damping is so small that it does not affect the solution accuracy nearly. The numerical examples show the instability phenomenon and indicate the effectiveness of the damping method. The time-domain stability studies here can be a reference for the other artificial boundary conditions.

scholarly journals Exact Artificial Boundary Conditions for Quasi-Linear Problems in Semi-Infinite Strips

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Yajun Chen ◽  
Qikui Du
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Finite Element Approximation ◽  
Element Approximation ◽  
Artificial Boundary ◽  
Numerical Examples ◽  
Artificial Boundary Conditions ◽  
Kirchhoff Transformation ◽  
Approximate Boundary Conditions ◽  
Linear Problems

In this paper, the exact artificial boundary conditions for quasi-linear problems in semi-infinite strips are investigated. Based on the Kirchhoff transformation, the exact and approximate boundary conditions on a segment artificial boundary are derived. The error estimate for the finite element approximation with the artificial boundary condition is obtained. Some numerical examples show the efficiency of this method.

scholarly journals Design of Broadband Dispersion Compensating Photonic Crystal Fiber

2012 ◽  
Vol 1 (4) ◽  
pp. 384 ◽  
Author(s):  
Md. Selim Habib ◽  
Md. Samiul Habib ◽  
S.M.A Razzak ◽  
M.A.G Khan
Keyword(s):  
Finite Element Method ◽  
Boundary Condition ◽  
Photonic Crystal ◽  
Photonic Crystal Fiber ◽  
Dispersion Coefficient ◽  
Dispersion Compensation ◽  
Design Parameters ◽  
The Finite Element Method ◽  
Crystal Fiber ◽  
Compensation Ratio

This paper presents a triangular-lattice photonic crystal fiber for broadband dispersion compensation. The finite element method with perfectly matched absorbing layers boundary condition is used to investigate the guiding properties. The designed dispersion compensating fiber shows that it is possible to obtain a larger negative dispersion coefficient of ?360 ps/(nm.km) at 1.55 ?m, better dispersion slope compensation, better compensation ratio in the entire telecommunication (1460-1640 nm) band by using a modest number of design parameters and very simple cladding design.

Transient Stokes Flow in a Wedge

1987 ◽  
Vol 54 (1) ◽  
pp. 203-208 ◽  
Author(s):  
Bohou Xu ◽  
E. B. Hansen
Keyword(s):  
Finite Element Method ◽  
Boundary Condition ◽  
Finite Element ◽  
Boundary Element Method ◽  
Circular Cylinder ◽  
Stokes Flow ◽  
Constant Velocity ◽  
Transient Flow ◽  
The Finite Element Method ◽  
Element Method

The transient flow in the sector region bounded by two intersecting planes and a circular cylinder is determined in the Stokes approximation. The plane boundaries are assumed to be at rest while the cylinder is rotating with a constant velocity starting at t = 0. The problem is solved by means of three different methods, a finite element, a finite difference, and a boundary element method. The corresponding problem in which the constant velocity boundary condition on the cylinder is replaced by a condition of constant stress is also solved by means of the finite element method.

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