The integral equations method with interface decomposition for the bi-harmonic
2
조회
0
다운로드
0
인용
0
참고문헌
초록
Abstract
Here, we will focus on domains decomposition methods based on thegeometry where the original boundary value problem is reduced to local sub-problems involving suitable matching conditions. In the present work, we apply this technic to the bi-harmonic with the Dirichlet conditions in two open and bounded sub-domains to be able to use the integral equations method with local boundaries. In each sub-domain, anintegral equations system is obtained after the application of the direct method based in the Green formula. By using boundary integral equations, we can solve this integral equations system. We will interpret that as pseudo-dierential operators, and via the symbolic computation of these operators, we can give the properties of these operators which allow us to establish the existence and the uniqueness of the solution.
참고문헌 (9)
- A, "Survey lectures on the mathematical foundations ofthe nite element method in the mathematical foundation of the finite element method with applications to partial dierential equations" (1972), AcademicPress
- Stephan, "On the boundary integral equa-tions of the first for the bilaplacien in polygonal plane domain Ann", scuola(rm), pp.~19 (1983)
- Stephan, "boundary integral equations for mixed boundaryvalue problems in polygonal domain and Galerkine approximation" (1985), Banach center publication
- Hildebrandt, "Constructive proofs of representation theorems in separable Hilbert space", pp.369~373 (1964)
- Kohn, "On the algebra of pseudo dierential operators" (1968)
- "Integral equation solution for simply supported polygonal plates" (1974)
- math, "on Boundary Element analysis of a direct methodfor the biharmonic Dirichlet problem" (1988)
- New York, "Introduction to pseudodierential and fourier integral operators" (1964), Plenom press
- S.E. Zarantonello, "Domain decomposition, boundary integrals and wavelets", 2569(1), pp.865~877 (1995)