Three-dimensional image-based modeling by combining SBFEM and transfinite element shape functions

The scaled boundary finite element method (SBFEM) has recently been employed as an efficient tool to model three-dimensional structures, in particular when the geometry is provided as a voxel-based image. To this end, an octree decomposition of the computational domain is deployed, and each cubic cell is treated as an SBFE subdomain. The surfaces of each subdomain are discretized in the finite element sense. We improve on this idea by combining the semi-analytical concept of the SBFEM with a particular class of transition elements on the subdomains’ surfaces. Thus, a triangulation of these surfaces as executed in previous works is avoided, and consequently, the number of surface elements and degrees of freedom is reduced. In addition, these discretizations allow coupling elements of arbitrary order such that local p-refinement can be achieved straightforwardly.

Finite-element analysis of infinite and finite arrays

This paper considers and compares the numerical characterization of regular planar antenna arrays from two viewpoints. In the case where the array is sufficiently large, the well-known infinite array idealization applies and a very efficient simulation method is presented which combines array theory with a specialized form of the finite-element method called the transfinite element method (TFEM). Alternatively, a more direct approach is discussed in which the entire antenna array is simulated as a finite structure using recent advances in the domain decomposition method (DDM). Taken together, the two methods provide a comprehensive simulation method for regular arrays from small order to very large order.