The Singular Function Boundary Integral Method for Elliptic Problems with Boundary Singularities

Christodoulou, Eirini; Xenophontos, Christos; Georgiou, Georgios C.

doi:10.1007/978-1-4020-9710-2_4

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Fig 2 Different Types Of Boundary Elements1

Bem For Constant Elements1

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2021

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“…Integrals of the type shown on the right hand side of (13) are easy to deal with as they present a lower order singularity, i.e. for three dimensional cases the integral around   gives: In other words nothing occurs to the right hand side integral when (10) or (13) are taken to the boundary . The left hand side integral however behaves in a different manner .…”

Section: Fig 2 Different Types Of Boundary Elementsmentioning

confidence: 99%

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A General Algorithm of the Boundary Integral Method for Solving Laplace’s Mixed Boundary Value Problem

Pal¹,

Kothiyal²,

Nigam³

2021

ARJOM

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Boundary elements have emerged as a powerful alternative to finite elements particularly in cases where better accuracy is required. The most important features of boundary elements however is that it only requires descretization of the surface rather than the volume. Here, A general algorithm of the boundary integral method has been formulated for solving elliptic partial differential equations. The broad applicability of the approach is illustrated with a problem of practical interest giving the solution of the Laplace equation for potential flow with mixed boundary problems. The results and patterns are shown in tables and figures and compared well with Brebbia [1] are found in good agreement.

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Section: Fig 2 Different Types Of Boundary Elementsmentioning

confidence: 99%

“…Once this is done it is possible to calculate any internal value of u or its derivatives. The values of u's are calculated at any internal point 'i' using formula (10) which can be written as,…”

Section: Bem For Constant Elementsmentioning

confidence: 99%