arXiv subjects

Leo C. Kempel

Publications and source records attributed to Leo C. Kempel.

3 recordsLinked to original sources

arXiv2023

A Transient Port-Extraction Technique for Antenna Feed Optimization

Optimization of strongly non-linear tightly coupled feeds attached to antennas is a challenging problem from a purely computational perspective. One can imagine that an optimization would (a) need to be in the time domain, and (b) has to be self-consistently coupled with the linear antenna (or electromagnetic) system. These two imply that the cost of optimization is governed by the need to repeatedly evaluate the fully coupled cost function. This paper leverages a recently developed transient port-extraction technique to circumvent this challenge and is agnostic to the optimization scheme. This approach provides a representation of the entire linear electromagnetic system at the port and can readily integrate with any non-linear circuit analysis and optimization methodology. In this paper, we demonstrate optimization of linear and non-linear circuit feed parameters that are tightly coupled to broadband radiating systems.

math.OC↗

arXiv2023

A Charge Conserving Exponential Predictor Corrector FEMPIC Formulation for Relativistic Particle Simulations

The state of art of charge-conserving electromagnetic finite element particle-in-cell has grown by leaps and bounds in the past few years. These advances have primarily been achieved for leap-frog time stepping schemes for Maxwell solvers, in large part, due to the method strictly following the proper space for representing fields, charges, and measuring currents. Unfortunately, leap-frog based solvers (and their other incarnations) are only conditionally stable. Recent advances have made Electromagnetic Finite Element Particle-in-Cell (EM-FEMPIC) methods built around unconditionally stable time stepping schemes were shown to conserve charge. Together with the use of a quasi-Helmholtz decomposition, these methods were both unconditionally stable and satisfied Gauss' Laws to machine precision. However, this architecture was developed for systems with explicit particle integrators where fields and velocities were off by a time step. While completely self-consistent methods exist in the literature, they follow the classic rubric: collect a system of first order differential equations (Maxwell and Newton equations) and use an integrator to solve the combined system. These methods suffer from the same side-effect as earlier--they are conditionally stable. Here we propose a different approach; we pair an unconditionally stable Maxwell solver to an exponential predictor-corrector method for Newton's equations. As we will show via numerical experiments, the proposed method conserves energy within a PIC scheme, has an unconditionally stable EM solve, solves Newton's equations to much higher accuracy than a traditional Boris solver and conserves charge to machine precision. We further demonstrate benefits compared to other polynomial methods to solve Newton's equations, like the well known Boris push.

math.NA↗

arXiv2022

Port Parameter Extraction Based Self Consistent Coupled EM-Circuit FEM Solvers

Self consistent solution to electromagnetic (EM)-circuit systems is of significant interest for a number of applications. This has resulted in exhaustive research on means to couple them. In time domain, this typically involves a tight integration (or coupling) with field and non-linear circuit solvers. This is in stark contrast to coupled analysis of linear/weakly non-linear circuits and EM systems in frequency domain. Here, one typically extracts equivalent port parameters that are then fed into the circuit solver. Such an approach has several advantages; (a) the number of ports is typically smaller than the number of degrees of freedom, resulting in cost savings; (b) is circuit agnostic; (c) can be integrated with a variety of device models. Port extraction is tantamount to obtaining impulse response of the linear EM system. In time domain, the deconvolution required to effect this is unstable. Recently, a novel approach was developed for time domain integral equations to overcome this bottleneck. We extend this approach to time domain finite element method, and demonstrate its utility via a number of examples; significantly, we demonstrate that self consistent solutions obtained using either a fully coupled or port extraction is identical to the desired precision for non-linear circuit systems. This is shown within a nodal network. We also demonstrate integration of port extracted data directly with drift diffusion equation to model device physics.

eess.SP↗