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## Solution of the radiation problem using isogeometric analysis

### Victoria Hernandez Mederos

#### Instituto de Cibernética Matemática y Física (ICIMAF), Cuba   -   This email address is being protected from spambots. You need JavaScript enabled to view it. document.getElementById('cloak6940db67ded0798a5331ce03e4a04004').innerHTML = ''; var prefix = '&#109;a' + 'i&#108;' + '&#116;o'; var path = 'hr' + 'ef' + '='; var addy6940db67ded0798a5331ce03e4a04004 = 'v&#105;cky' + '&#64;'; addy6940db67ded0798a5331ce03e4a04004 = addy6940db67ded0798a5331ce03e4a04004 + '&#105;c&#105;m&#97;f' + '&#46;' + 'c&#117;'; var addy_text6940db67ded0798a5331ce03e4a04004 = 'v&#105;cky' + '&#64;' + '&#105;c&#105;m&#97;f' + '&#46;' + 'c&#117;';document.getElementById('cloak6940db67ded0798a5331ce03e4a04004').innerHTML += '<a ' + path + '\'' + prefix + ':' + addy6940db67ded0798a5331ce03e4a04004 + '\'>'+addy_text6940db67ded0798a5331ce03e4a04004+'<\/a>';

We discuss the numerical solution of the 2D Helmoltz equation with mixed boundary conditions, defining the so called radiation problem. This problem depends on a constant parameter k, the wavenumber. For relative small values of k, the radiation problem can be handled with low order Finite Element Method (FEM). But in modern medical and industrial applications the values of k can be of order of thousands, and several numerical difficulties appear. To overcome these difficulties we solve the radiation problem using the isogeometric method, a kind of generalization of the classic FEM based on B-splines functions. Our numerical experiments show that isogeometric approach is superior than the classic FEM reducing significatively the pollution error, especially for high values of k.

Joint work with Eduardo Moreno Hernandez (ICIMAF, Cuba), Jorge Estrada Sarlabous (ICIMAF, Cuba), Isidro Abello Ugalde (Universidad de La Habana, Cuba) and Domenico Lahaye ( DIAM TU Delf, The Netherlands).