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Domain Integrals
| Content Provider | Scilit |
|---|---|
| Author | Kythe, Prem K. |
| Copyright Year | 2020 |
| Description | Book Name: An introduction to BOUNDARY ELEMENT METHODS |
| Abstract | The domain integrals arise in the BE formulation for the potential, elastostatic, and other problems. Thus, for example, in the Poisson problem (5.65)–(5.66), the function b(x) produces the domain integral (5.71), i.e., (9.1) B i = ∬ R b u ∗ d x d y , which appears in the BE Eq (5.70). In elastostatic problems, if the body forces are present, we encounter the domain integral (6.45), i.e., (9.2) B i = ∬ R ˜ b u ∗ d x 1 d x 2 , which is present in the related BE Eq (6.44). In the case of forced oscillations the governing equation is (9.3) ( ∇ 2 + k 2 ) u = b , where k = ω/c is the wave number, and b is a function of space variables that measures the yield of the sources which may be continuously disturbed or concentrated in a single point. The function b must vanish at infinity. If b = 0, Eq (9.3) reduces to the Helmholtz equation (7.37). The BE Eq for (9.3) will also lead to a domain integral of the form (9.1). The domain integral (8.4) which is of the same type as (9.1) also appears in aerodynamic flows around lifting bodies and in flows through porous media defined by (8.31). The interior cell method developed in §5.7 is not a powerful method to numerically compute the domain integrals. This method involves an interior discretization and evaluation of the double integral over each interior cell, which in turn increases the numerical data considerably and thus diminishes the computational advantage that the BEM has over other domain–type methods. 264the double integral over each interior cell, which in turn increases the numerical data considerably and thus diminishes the computational advantage that the BEM has over other domain–type methods. In order to avoid the cumbersome situation created by the interior cell method we must have a method that enables a boundary–only solution instead of the domain integrals and is applicable to similar problems whenever they arise. There are three different methods available at present to transform the domain integrals into boundary integrals. These methods have historically evolved as follows: (i) Dual reciprocity method (DRM), (ii) Fourier series expansion method (FSM), and (iii) Multiple reciprocity method (MRM). We shall now present them in that order. |
| Related Links | https://content.taylorfrancis.com/books/download?dac=C2006-0-08535-3&isbn=9781003068693&doi=10.1201/9781003068693-10&format=pdf |
| Ending Page | 290 |
| Page Count | 28 |
| Starting Page | 263 |
| DOI | 10.1201/9781003068693-10 |
| Language | English |
| Publisher | Informa UK Limited |
| Publisher Date | 2020-11-25 |
| Access Restriction | Open |
| Subject Keyword | Book Name: An introduction to BOUNDARY ELEMENT METHODS Mathematical Physics Domain Integral Interior Cell |
| Content Type | Text |
| Resource Type | Chapter |
