Solving large complex problems using a higher order basis: Parallel out-of-core integral equation solvers involving a million unknowns

The future of computational electromagnetics is CHANGING DRASTICALLY with the new generation of computer chips which are multi-core instead of single core. Previously, advancements in chip technology meant an increase in clock speed, which was typically a benefit that computational code users could enjoy. This is no longer the case. In the new roadmaps for chip manufacturers, speed has been sacrificed for improved power consumption and the direction is multi-core processors. The burden now falls on the software programmer to revamp existing codes and add new functionality to enable computational codes to run efficiently on this new generation of multi-core processors. In this paper, a new roadmap for computational code designers is provided, demonstrating how to navigate along with the chip designers through the multi-core advancements in chip design. A new parallel out-of-core solver code termed HOBBIES using the Method of Moments (MoM) and higher order functions for expansion and testing will illustrate this roadmap. The advantage of a higher order basis over a subdomain basis is a reduction in the number of unknowns. This means that with the same computer resources, a larger problem can be solved using higher order basis than using a subdomain basis. It is illustrated how to solve a million by million complex matrix equation using a parallel out-of-core solver using modest computational resources.