Boundary Hybrid Galerkin Method for Elliptic and Wave Propagation Problems in ℝ3 over Planar Structures

Jerez-Hanckes, Carlos; Nédélec, Jean-Claude

doi:10.1007/978-0-8176-4897-8_19

Cited by 1 publication

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“…The difficulty of the problem is that the solution is continuous at the tips, but its gradient may have weak singularity. Numerical methods of problems are considered in Hölder space in a series of papers [1][2][3]. The analysis in [4] is performed within a Sobolev space setting and a weak solution concept, but no numerical method is presented.…”

Section: Introductionmentioning

confidence: 99%

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Boundary Galerkin Method of a Skew-Derivative Problem in the Exterior of an Open Arc Based on Chebyshev Polynomials

Sun

2013

Mathematical Problems in Engineering

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A problem modeling Hall effect in a semiconductor film from an electrode of arbitrary shape is considered, which is a skew-derivative problem. Boundary Galerkin method for solving the problem in Sobolev spaces is developed firstly. The solution is represented in the form of the combined angular potential and single-layer potential. The final integral equations do not contain hypersingular integrals. Uniqueness and existence of the solution to the equations are proved. The weakly singular and Cauchy singular integral arising in these equations can be computed directly by truncated series of Chebyshev polynomials with their weighting function without approximation. The numerical simulation showing the high accuracy of the scheme is presented.

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Section: Introductionmentioning

confidence: 99%

“…The purpose of this paper is to develop an efficient solution method. Due to the properties of Chebyshev polynomials, several researchers [1,3] use them for solving integral equations. In this paper, we approximate the unknown function by means of truncated series of Chebyshev polynomials with their weighting function.…”

Section: Introductionmentioning

confidence: 99%

Boundary Galerkin Method of a Skew-Derivative Problem in the Exterior of an Open Arc Based on Chebyshev Polynomials

Sun

2013

Mathematical Problems in Engineering

View full text Add to dashboard Cite

show abstract

Boundary Hybrid Galerkin Method for Elliptic and Wave Propagation Problems in ℝ3 over Planar Structures

Cited by 1 publication

References 7 publications

Boundary Galerkin Method of a Skew-Derivative Problem in the Exterior of an Open Arc Based on Chebyshev Polynomials

Boundary Galerkin Method of a Skew-Derivative Problem in the Exterior of an Open Arc Based on Chebyshev Polynomials

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