报告题目：Artificial neural network methods for boundary integral equations
报 告 人：Elena Atroshchenko博士，澳大利亚新南威尔士大学
In this talk, we present approximation of boundary integral equations (BIEs) by using deep neural networks with unknown weights and biases, trained to minimise the BIE error at a set of collocation points. The boundary is parameterized with NURBS basis functions, which allows accurate evaluation of such geometrical parameters, as normal vectors and Jacobians. Singularity subtraction technique to integrate singular kernels is also adopted from a standard boundary element method. The method inherits all main advantages of BIE-type methods, such as reduced size of the problem and the ability to easily model solutions in unbounded domains. Some important limitations of the method are large computational time and the availability of Green function. Performance of the method is demonstrated on several benchmark examples for Laplace equation and problems of linear elasticity.
Dr. Elena Atroshchenko obtained her PhD from the University of Waterloo, Ontario, Canada in 2010. From 2012 until 2018, she held a position of an Assistant Professor in the department of Mechanical Engineering, University of Chile, Santiago, Chile. In January 2019 she joined School of Civil and Environmental Engineering at University of New South Wales, Sydney, Australia in the role of a Senior Lecturer. Her research interests lie in the field of computational mechanics, with main focus on isogeometric and generalized isogeometric analysis, boundary element method, fracture mechanics, acoustics, shape and topology optimization.