ON THE COMPUTATION OF SINGULAR INTEGRALS OVER TRIANGULAR SURFACES IN R3
Author(s)
HRVOJE DODIG, MARIO CVETKOVIĆ, DRAGAN POLJAK
Abstract
Various integral equation formulations and the related numerical solutions either via Boundary Element Method (BEM) or Method of Moments (MoM) require tedious calculation of double surface integrals arising from the use of vector triangular basis functions. This paper presents an accurate technique for computation of these integrals by first converting the surface integrals to contour integrals facilitating the decomposition of boundary integral to the sum of line integrals over triangle edges. It was shown that application of this technique to a Laplace type of equations yields expressions having analytical solutions. Moreover, although the same was not possible to achieve in case of integrals involving Helmholtz kernels, nonetheless, the technique enabled the computation of surface integrals to a machine accuracy by employing the adaptive quadrature rules. This approach could be found useful in the high frequency computational dosimetry.
Keywords
boundary element method, Helmholtz equation, Laplace equation, adaptive quadrature, contour integrals
Related Book
Other papers in this volume
Warning (2)
: foreach() argument must be of type array|object, null given [in
/var/www/dce7ae55-385b-4ffa-8595-3ec5e61ff110/public_html/app/templates/Papers/view.php, line
364]
Code
$counter = '0';
foreach ($paper['book']['Paper'] as $otherPaper) {
if ((!empty($otherPaper['name'])) && ($counter < '7') && ($otherPaper['available'] == 1)) {
Cake\Error\ErrorTrap->handleError() /var/www/dce7ae55-385b-4ffa-8595-3ec5e61ff110/public_html/app/templates/Papers/view.php, line 364
/var/www/dce7ae55-385b-4ffa-8595-3ec5e61ff110/public_html/app/vendor/cakephp/cakephp/src/View/View.php /var/www/dce7ae55-385b-4ffa-8595-3ec5e61ff110/public_html/app/vendor/cakephp/cakephp/src/View/View.php, line 1188
Cake\View\View->_evaluate() /var/www/dce7ae55-385b-4ffa-8595-3ec5e61ff110/public_html/app/vendor/cakephp/cakephp/src/View/View.php, line 1145
Cake\View\View->_render() /var/www/dce7ae55-385b-4ffa-8595-3ec5e61ff110/public_html/app/vendor/cakephp/cakephp/src/View/View.php, line 785
Cake\View\View->render() /var/www/dce7ae55-385b-4ffa-8595-3ec5e61ff110/public_html/app/vendor/cakephp/cakephp/src/Controller/Controller.php, line 712
Cake\Controller\Controller->render() /var/www/dce7ae55-385b-4ffa-8595-3ec5e61ff110/public_html/app/vendor/cakephp/cakephp/src/Controller/Controller.php, line 516
Cake\Controller\Controller->invokeAction() /var/www/dce7ae55-385b-4ffa-8595-3ec5e61ff110/public_html/app/vendor/cakephp/cakephp/src/Controller/ControllerFactory.php, line 166
Cake\Controller\ControllerFactory->handle() /var/www/dce7ae55-385b-4ffa-8595-3ec5e61ff110/public_html/app/vendor/cakephp/cakephp/src/Controller/ControllerFactory.php, line 141
Cake\Controller\ControllerFactory->invoke() /var/www/dce7ae55-385b-4ffa-8595-3ec5e61ff110/public_html/app/vendor/cakephp/cakephp/src/Http/BaseApplication.php, line 362
Cake\Http\BaseApplication->handle() /var/www/dce7ae55-385b-4ffa-8595-3ec5e61ff110/public_html/app/vendor/cakephp/cakephp/src/Http/Runner.php, line 86
Cake\Http\Runner->handle() /var/www/dce7ae55-385b-4ffa-8595-3ec5e61ff110/public_html/app/vendor/cakephp/cakephp/src/Http/Middleware/CsrfProtectionMiddleware.php, line 169
Cake\Http\Middleware\CsrfProtectionMiddleware->process() /var/www/dce7ae55-385b-4ffa-8595-3ec5e61ff110/public_html/app/vendor/cakephp/cakephp/src/Http/Runner.php, line 82
Cake\Http\Runner->handle() /var/www/dce7ae55-385b-4ffa-8595-3ec5e61ff110/public_html/app/vendor/cakephp/cakephp/src/Http/Middleware/BodyParserMiddleware.php, line 157
Cake\Http\Middleware\BodyParserMiddleware->process() /var/www/dce7ae55-385b-4ffa-8595-3ec5e61ff110/public_html/app/vendor/cakephp/cakephp/src/Http/Runner.php, line 82
Cake\Http\Runner->handle() /var/www/dce7ae55-385b-4ffa-8595-3ec5e61ff110/public_html/app/vendor/cakephp/cakephp/src/Routing/Middleware/RoutingMiddleware.php, line 118
Cake\Routing\Middleware\RoutingMiddleware->process() /var/www/dce7ae55-385b-4ffa-8595-3ec5e61ff110/public_html/app/vendor/cakephp/cakephp/src/Http/Runner.php, line 82
Cake\Http\Runner->handle() /var/www/dce7ae55-385b-4ffa-8595-3ec5e61ff110/public_html/app/vendor/cakephp/cakephp/src/Routing/Middleware/AssetMiddleware.php, line 69
Cake\Routing\Middleware\AssetMiddleware->process() /var/www/dce7ae55-385b-4ffa-8595-3ec5e61ff110/public_html/app/vendor/cakephp/cakephp/src/Http/Runner.php, line 82
Cake\Http\Runner->handle() /var/www/dce7ae55-385b-4ffa-8595-3ec5e61ff110/public_html/app/vendor/cakephp/cakephp/src/Error/Middleware/ErrorHandlerMiddleware.php, line 115
Cake\Error\Middleware\ErrorHandlerMiddleware->process() /var/www/dce7ae55-385b-4ffa-8595-3ec5e61ff110/public_html/app/vendor/cakephp/cakephp/src/Http/Runner.php, line 82
Cake\Http\Runner->handle() /var/www/dce7ae55-385b-4ffa-8595-3ec5e61ff110/public_html/app/vendor/cakephp/debug_kit/src/Middleware/DebugKitMiddleware.php, line 60
DebugKit\Middleware\DebugKitMiddleware->process() /var/www/dce7ae55-385b-4ffa-8595-3ec5e61ff110/public_html/app/vendor/cakephp/cakephp/src/Http/Runner.php, line 82
Cake\Http\Runner->handle() /var/www/dce7ae55-385b-4ffa-8595-3ec5e61ff110/public_html/app/vendor/cakephp/cakephp/src/Http/Runner.php, line 60
Cake\Http\Runner->run() /var/www/dce7ae55-385b-4ffa-8595-3ec5e61ff110/public_html/app/vendor/cakephp/cakephp/src/Http/Server.php, line 104
Cake\Http\Server->run() /var/www/dce7ae55-385b-4ffa-8595-3ec5e61ff110/public_html/app/webroot/index.php, line 37
[main]
