Efficient Solutions for Nonlocal Diffusion Problems Via Boundary-Adapted Spectral Methods
Efficient Solutions for Nonlocal Diffusion Problems Via Boundary-Adapted Spectral Methods
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DOI：
10.1007/s42102-019-00026-6
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发表时间：
2019-05
期刊：
影响因子：
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通讯作者：
S. Jafarzadeh;Adam Larios;F. Bobaru
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文献类型：
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作者：
S. Jafarzadeh;Adam Larios;F. Bobaru
本文介绍了一种有效的边界适应谱方法来求解具有任意边界条件的周期瞬态扩散问题。谱方法将周波公式中的卷积积分转换为傅立叶空间中的乘法，导致计算的规模阿索（NlogN）。利用体积惩罚法消除了正则谱方法对周期问题的局限性。我们表明，任意的边界条件或体积约束，可以强制执行以这种方式实现高水平的精度。为了测试我们的方法的性能，我们比较的非局部问题的解析解的计算结果。的性能进行了测试，收敛性研究的节点离散化和惩罚参数的大小与Dirichlet和Neumann边界条件的问题。
We introduce an efficient boundary-adapted spectral method for peridynamic transient diffusion problems with arbitrary boundary conditions. The spectral approach transforms the convolution integral in the peridynamic formulation into a multiplication in the Fourier space, resulting in computations that scale asO(NlogN). The limitation of regular spectral methods to periodic problems is eliminated using the volume penalization method. We show that arbitrary boundary conditions or volume constraints can be enforced in this way to achieve high levels of accuracy. To test the performance of our approach we compare the computational results with analytical solutions of the nonlocal problem. The performance is tested with convergence studies in terms of nodal discretization and the size of the penalization parameter in problems with Dirichlet and Neumann boundary conditions.