کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
513063 866448 2013 8 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Adaptive cross approximation of tensors arising in the discretization of boundary integral operator shape derivatives
موضوعات مرتبط
مهندسی و علوم پایه مهندسی کامپیوتر نرم افزارهای علوم کامپیوتر
پیش نمایش صفحه اول مقاله
Adaptive cross approximation of tensors arising in the discretization of boundary integral operator shape derivatives
چکیده انگلیسی

The shape derivative of a dense N×N BEM matrix is a sparse three-way tensor with O(N2) non-zero entries, to which standard BEM acceleration techniques such as the adaptive cross approximation (ACA) and FMM cannot be directly applied. The tensor can be used to compute shape sensitivities, or via adjoint equations, the gradient of an objective function. Although for many PDEs, calculation of the tensor can be avoided by expressing the shape derivative of the solution as the solution of a related PDE, this approach is not always easily amenable to BEM. Therefore, the computation of shape derivatives via the sparse three-way tensor is a valuable alternative, provided that efficient acceleration techniques exist. We propose a new algorithm for the approximation of BEM shape derivative tensors based on ACA that achieves the same complexity and error bounds as ACA for the BEM matrix itself. Numerical examples show that despite the much larger amount of data involved, the tensor approximation is only moderately slower than the matrix approximation. We also demonstrate the method on a shape optimization problem from the literature.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Engineering Analysis with Boundary Elements - Volume 37, Issue 1, January 2013, Pages 60–67
نویسندگان
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