Three-Dimensional Volume Integral Equation Method for Solving Isotropic/Anisotropic Inhomogeneity Problems

Abstract

In this paper, the volume integral equation method (VIEM) is introduced for the analysis of an unbounded isotropic solid composed of multiple isotropic/anisotropic inhomogeneities. A comprehensive examination of a three-dimensional elastostatic VIEM is introduced for the analysis of an unbounded isotropic solid composed of isotropic/anisotropic inhomogeneity of arbitrary shape. The authors hope that the volume integral equation method can be used to compute critical values of practical interest in realistic models of composites composed of strong anisotropic and/or heterogeneous inhomogeneities of arbitrary shapes.

Volume Integral Equation Method Solution for Spheroidal Inclusion Problem

“…The volume integral equation method (VIEM) was originated from Lee and Mal [10] in 1995. Since 1995, Lee and his co-workers (e.g., [9][10][11][13][14][15][16][17]) have been developing a more engineering-oriented VIEM, while Buryachenko (e.g., [18][19][20]) has been examining a more mathematically oriented VIEM since 2000. Additionally, Dong has conducted research on the volume integral equation method since 2003 [21].…”

“…) [22]. In addition, complete descriptions of the fundamental numerical technique of Equation ( 2) can be found in [17] for three-dimensional elastostatic problems.…”

“…Such method allows us not only to solve the large domain but also to speed up computation in the volume integral equation method. The FORTRAN 90 (Version 1.1, IBM, Armonk, NY, USA) source code containing about 9000 lines for the three-dimensional VIEM of the previous paper [17] was parallelized and optimized for this paper, with support from the Korea Institute of Science and Technology Information (KISTI, Daejeon, Korea). Figure 2 shows the procedures of a representative MPI parallelization approach ("pvi3ds01_sm7560xx.f90") for the sequential three-dimensional VIEM code ("svi3ds01_sm4320xx.f").…”

“…As a result, the program execution time has been greatly reduced. Furthermore, we could use more finite elements (31,857 nodes and 7560 elements) in the VIEM model of this paper than those (18,109 nodes and 4320 elements) in the VIEM model of the previous paper [17]. The parallel FORTRAN source code for the three-dimensional VIEM is presently being processed in the KISTI-5.…”

“…A comprehensive elaboration for the accurate evaluation of singular integrals using the tetrahedron polar co-ordinates shown in [29] was presented in [17].…”