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Indian Institute of Science

1. Das, Arkaprovo. Fast Solvers for Integtral-Equation based Electromagnetic Simulations.

Degree: PhD, Faculty of Engineering, 2018, Indian Institute of Science

With the rapid increase in available compute power and memory, and bolstered by the advent of efficient formulations and algorithms, the role of 3D full-wave computational methods for accurate modelling of complex electromagnetic (EM) structures has gained in significance. The range of problems includes Radar Cross Section (RCS) computation, analysis and design of antennas and passive microwave circuits, bio-medical non-invasive detection and therapeutics, energy harvesting etc. Further, with the rapid advances in technology trends like System-in-Package (SiP) and System-on-Chip (SoC), the fidelity of chip-to-chip communication and package-board electrical performance parameters like signal integrity (SI), power integrity (PI), electromagnetic interference (EMI) are becoming increasingly critical. Rising pin-counts to satisfy functionality requirements and decreasing layer-counts to maintain cost-effectiveness necessitates 3D full wave electromagnetic solution for accurate system modelling. Method of Moments (MoM) is one such widely used computational technique to solve a 3D electromagnetic problem with full-wave accuracy. Due to lesser number of mesh elements or discretization on the geometry, MoM has an advantage of a smaller matrix size. However, due to Green's Function interactions, the MoM matrix is dense and its solution presents a time and memory challenge. The thesis focuses on formulation and development of novel techniques that aid in fast MoM based electromagnetic solutions. With the recent paradigm shift in computer hardware architectures transitioning from single-core microprocessors to multi-core systems, it is of prime importance to parallelize the serial electromagnetic formulations in order to leverage maximum computational benefits. Therefore, the thesis explores the possibilities to expedite an electromagnetic simulation by scalable parallelization of near-linear complexity algorithms like Fast Multipole Method (FMM) on a multi-core platform. Secondly, with the best of parallelization strategies in place and near-linear complexity algorithms in use, the solution time of a complex EM problem can still be exceedingly large due to over-meshing of the geometry to achieve a desired level of accuracy. Hence, the thesis focuses on judicious placement of mesh elements on the geometry to capture the physics of the problem without compromising on accuracy- a technique called Adaptive Mesh Refinement. This facilitates a reduction in the number of solution variables or degrees of freedom in the system and hence the solution time. For multi-scale structures as encountered in chip-package-board systems, the MoM formulation breaks down for parts of the geometry having dimensions much smaller as compared to the operating wavelength. This phenomenon is popularly known as low-frequency breakdown or low-frequency instability. It results in an ill-conditioned MoM system matrix, and hence higher iteration count to converge when solved using an iterative solver framework. This consequently increases the solution time… Advisors/Committee Members: Gope, Dipanjan (advisor).

Subjects/Keywords: Electromagnetic Solvers; Method of Moments (MOM); Electromagnetic Simulations; Computational Electromagnetics; Electromagnetics; Fast Multiple Method; Adaptive Mesh Refinement; Integral Equation Electromagnetic Solvers; Electromagnetic Refinement Indicators; Electric Field Integral Equation; Electrical Communication Engineering

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APA (6th Edition):

Das, A. (2018). Fast Solvers for Integtral-Equation based Electromagnetic Simulations. (Doctoral Dissertation). Indian Institute of Science. Retrieved from

Chicago Manual of Style (16th Edition):

Das, Arkaprovo. “Fast Solvers for Integtral-Equation based Electromagnetic Simulations.” 2018. Doctoral Dissertation, Indian Institute of Science. Accessed April 12, 2021.

MLA Handbook (7th Edition):

Das, Arkaprovo. “Fast Solvers for Integtral-Equation based Electromagnetic Simulations.” 2018. Web. 12 Apr 2021.


Das A. Fast Solvers for Integtral-Equation based Electromagnetic Simulations. [Internet] [Doctoral dissertation]. Indian Institute of Science; 2018. [cited 2021 Apr 12]. Available from:

Council of Science Editors:

Das A. Fast Solvers for Integtral-Equation based Electromagnetic Simulations. [Doctoral Dissertation]. Indian Institute of Science; 2018. Available from: