Fast numerical method for computing resonant characteristics of electromagnetic devices based on finite element method

2016 ◽  
Author(s):  
Xiu Zhang ◽  
W. N. Fu ◽  
S. X. Niu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Method ◽  
Electromagnetic Devices ◽  
Element Method

scholarly journals An Eulerian finite element method for PDEs in time-dependent domains

2019 ◽  
Vol 53 (2) ◽  
pp. 585-614 ◽  
Author(s):  
Christoph Lehrenfeld ◽  
Maxim Olshanskii
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Finite Difference ◽  
Numerical Method ◽  
Computational Domain ◽  
Physical Domain ◽  
Finite Element Approximations ◽  
Additional Stabilization ◽  
Background Mesh ◽  
Element Method

The paper introduces a new finite element numerical method for the solution of partial differential equations on evolving domains. The approach uses a completely Eulerian description of the domain motion. The physical domain is embedded in a triangulated computational domain and can overlap the time-independent background mesh in an arbitrary way. The numerical method is based on finite difference discretizations of time derivatives and a standard geometrically unfitted finite element method with an additional stabilization term in the spatial domain. The performance and analysis of the method rely on the fundamental extension result in Sobolev spaces for functions defined on bounded domains. This paper includes a complete stability and error analysis, which accounts for discretization errors resulting from finite difference and finite element approximations as well as for geometric errors coming from a possible approximate recovery of the physical domain. Several numerical examples illustrate the theory and demonstrate the practical efficiency of the method.

Variational multi-scale finite element method for the two-phase flow of polymer melt filling process

2019 ◽  
Vol 30 (3) ◽  
pp. 1407-1426 ◽  
Author(s):  
Xuejuan Li ◽  
Ji-Huan He
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Method ◽  
Two Phase Flow ◽  
Polymer Melt ◽  
Phase Flow ◽  
Filling Process ◽  
Two Phase ◽  
Content Type ◽  
Element Method

Purpose The purpose of this paper is to develop an effective numerical algorithm for a gas-melt two-phase flow and use it to simulate a polymer melt filling process. Moreover, the suggested algorithm can deal with the moving interface and discontinuities of unknowns across the interface. Design/methodology/approach The algebraic sub-grid scales-variational multi-scale (ASGS-VMS) finite element method is used to solve the polymer melt filling process. Meanwhile, the time is discretized using the Crank–Nicolson-based split fractional step algorithm to reduce the computational time. The improved level set method is used to capture the melt front interface, and the related equations are discretized by the second-order Taylor–Galerkin scheme in space and the third-order total variation diminishing Runge–Kutta scheme in time. Findings The numerical method is validated by the benchmark problem. Moreover, the viscoelastic polymer melt filling process is investigated in a rectangular cavity. The front interface, pressure field and flow-induced stresses of polymer melt during the filling process are predicted. Overall, this paper presents a VMS method for polymer injection molding. The present numerical method is extremely suitable for two free surface problems. Originality/value For the first time ever, the ASGS-VMS finite element method is performed for the two-phase flow of polymer melt filling process, and an effective numerical method is designed to catch the moving surface.

A FINITE ELEMENT METHOD FOR MODELING OF ELECTROMAGNETIC PROBLEMS

2020 ◽  
pp. 25-31
Author(s):  
Vuong
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Magnetic Flux Density ◽  
Analytic Method ◽  
Electrical System ◽  
Electromagnetic Problems ◽  
Magnetic Circuits ◽  
Electromagnetic Devices ◽  
Electrical Devices ◽  
Element Method

Electromagnetic devices are present everywhere in our daily life. In particular, they extremely play an important role  in the fields of the electrical system. Therefore, the modeling and analyzing the electromagetic problems become currently a matter of concern and topicality for researchers and designers of electrical devices. This paper introduces a finite element method to compute accurate distributions of leakage and fringing fluxes with air-gap variations, and eddy current losses of the magnetic circuits, that cannot generally be solved by a direct analytic method. The method is approached for the magnetic flux density formulation.

An Analysis of the Large Deflections of Beams using the Rayleigh-Ritz Finite Element Method

1968 ◽  
Vol 19 (4) ◽  
pp. 357-367 ◽  
Author(s):  
A. C. Walker ◽  
D. G. Hall
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Method ◽  
Large Deflection ◽  
Energy Functional ◽  
Algebraic Equations ◽  
Linear Algebraic Equations ◽  
Non Linear ◽  
Comparison Of The Results ◽  
Element Method

SummaryThe Rayleigh-Ritz finite element method is used to obtain an approximate solution of the exact non-linear energy functional describing the large deflection bending behaviour of a simply-supported inextensible uniform beam subjected to point loads. The solution of the non-linear algebraic equations resulting from the use of this method is effected, using three different techniques, and comparisons are made regarding the accuracy and computing effort involved in each. A description is given of an experimental investigation of the problem and comparison of the results with those of the numerical method, and of the available exact continuum analyses, indicates that the numerical method provides satisfactory predictions for the non-linear beam behaviour for deflections up to one quarter of the beam’s length.

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