Benchmarking Numerical Computation of the First-order Polarization Tensor in Low Conductive Materials

Abstract

The study of the behaviour of conductive materials responding to electromagnetic fields is a key to the development in the field of materials science and engineering. Polarization Tensor (PT) provides the information regarding the shape, orientation and the material properties of an object. Current numerical techniques tend to be fast at the expense of accuracy leading to slowness to converge or expensive computation. This paper presents a simplified numerical approach, which will evaluate the first-order PT in three-dimensional, more efficiently and accurately. The discretization of the geometry is performed using free software which are Netgen Mesh Generator and MATLAB. Adaptive methods are used to shapes such as spheres and cubes, such as the selective mesh refinement are comparing 1-point and 3-point integration to achieve the optimum balance. The analytical solution of spherical geometry is used to validate proposed method. The use of adaptive mesh refinement with a matrix calculation method is much faster and more accurate in calculating PT. All these enhancements are on the whole a sensible step in the direction of simulating complex materials and forms a high-performance baseline on the real world applications such as medical imaging and industrial testing. The results show that the adaptive approach is a good and scalable method of computing the PT of complex conducting materials.