Seamless-domain method: a meshfree multiscale numerical analysis
Yoshiro Suzuki, Kosuke Soga · International Journal for Numerical Methods in Engineering · 2015
A new numerical scheme, termed the seamless-domain method (SDM), is applied in a multiscale technique. The SDM requires only points and does not require a stiffness equation, mesh, grid, cell, or element. The SDM consists of two steps. The first step is a microscopic analysis of the local (small) simulation domain to obtain interpolation functions for discretizing governing equations. This allows an SDM solution to represent a heterogeneous material with microscopic constituents without homogenization. The second step is a macroscopic analysis of a seamless global (entire) domain that has no mesh and only coarse-grained points. The special functions obtained in the first step are used in interpolating the continuous dependent-variable distribution in the seamless global domain whose gradient is also continuous everywhere. The SDM would give a quite accurate solution for domains with strong boundary effects, anisotropic and heterogeneous materials, and isotropic homogeneous fields. Numerical examples of steady-state heat conduction fields are presented. For heterogeneous material, the SDM using only 117 points provided solutions as accurate as those of the traditional finite element method using 21,665 nodes. Analysis of an isotropic material verified the cost effectiveness of the SDM as in the analysis of heterogeneous material. Copyright © 2015 John Wiley & Sons, Ltd. John Wiley & Sons, Ltd.