GPU Accelerated Explicit Time Integration Methods for Electro-Quasistatic Fields

Electro-quasistatic field problems involving nonlinear materials are commonly discretized in space using finite elements. In this paper, it is proposed to solve the resulting system of ordinary differential equations by an explicit Runge-Kutta-Chebyshev time-integration scheme. This mitigates the need for Newton-Raphson iterations, as they are necessary within fully implicit time integration schemes. However, the electro-quasistatic system of ordinary differential equations has a Laplace-type mass matrix such that parts of the explicit time-integration scheme remain implicit. An iterative solver with constant preconditioner is shown to efficiently solve the resulting multiple right-hand side problem. This approach allows an efficient parallel implementation on a system featuring multiple graphic processing units.Comment: 4 pages, 5 figure

Systems of Differential Algebraic Equations in Computational Electromagnetics

Starting from space-discretisation of Maxwell's equations, various classical formulations are proposed for the simulation of electromagnetic fields. They differ in the phenomena considered as well as in the variables chosen for discretisation. This contribution presents a literature survey of the most common approximations and formulations with a focus on their structural properties. The differential-algebraic character is discussed and quantified by the differential index concept

The Partial Elements Equivalent Circuit Method: The State Of The Art

This year marks about half a century since the birth of the technique known as the partial element equivalent circuit modeling approach. This method was initially conceived to model the behavior of interconnect-type problems for computer-integrated circuits. An important industrial requirement was the computation of general inductances in integrated circuits and packages. Since then, the advances in methods and applications made it suitable for modeling a large class of electromagnetic problems, especially in the electromagnetic compatibility (EMC)/signal and power integrity (SI/PI) areas. The purpose of this article is to present an overview of all aspects of the method, from its beginning to the present day, with special attention to the developments that have made it suitable for EMC/SI/PI problems

Roadmap on multiscale materials modeling

Modeling and simulation is transforming modern materials science, becoming an important tool for the discovery of new materials and material phenomena, for gaining insight into the processes that govern materials behavior, and, increasingly, for quantitative predictions that can be used as part of a design tool in full partnership with experimental synthesis and characterization. Modeling and simulation is the essential bridge from good science to good engineering, spanning from fundamental understanding of materials behavior to deliberate design of new materials technologies leveraging new properties and processes. This Roadmap presents a broad overview of the extensive impact computational modeling has had in materials science in the past few decades, and offers focused perspectives on where the path forward lies as this rapidly expanding field evolves to meet the challenges of the next few decades. The Roadmap offers perspectives on advances within disciplines as diverse as phase field methods to model mesoscale behavior and molecular dynamics methods to deduce the fundamental atomic-scale dynamical processes governing materials response, to the challenges involved in the interdisciplinary research that tackles complex materials problems where the governing phenomena span different scales of materials behavior requiring multiscale approaches. The shift from understanding fundamental materials behavior to development of quantitative approaches to explain and predict experimental observations requires advances in the methods and practice in simulations for reproducibility and reliability, and interacting with a computational ecosystem that integrates new theory development, innovative applications, and an increasingly integrated software and computational infrastructure that takes advantage of the increasingly powerful computational methods and computing hardware

Time evolution of the electric field by the rapid expansion method in controlled-source electromagnetic (CSEM) applications

I address the problem of modelling the low-frequency, time-domain controlled-source electromagnetic (CSEM) data by the rapid expansion method (REM). The CSEM method is an active EM exploration method that is recognized as complementary to the seismic method, with the focus on determining subsurface electric resistivity. Interpretation of CSEM data relies on an iterative forward modelling process to search for the model that best fits the data. Therefore, forward modelling is an essential part of the interpretation process. REM is an explicit time-domain forward modelling method that solves the diffusive EM field based on a Chebyshev expansion of the time operator. The temporal estimator is accurate to the Nyquist frequency and temporal numerical dispersion can be mitigated. I present several extensions of the REM algorithm to generalize its use in various environments. I show the response from the Earth-air interface can be modelled by solving the air field explicitly in the Chebyshev domain. I show that transverse isotropic anisotropy can be included in the modelling with the manipulation of the conductivity tensor. I show that by introducing another fictitious series of Chebyshev polynomials, the updating of Chebyshev terms is equivalent to coupled EM wave equations in a vacuum. EM wavefield modelling techniques can therefore be transferred to the Chebyshev domain, and I show the use of perfectly matched layers, a well-established absorbing boundary condition designed for EM waves, to solve the numerical boundary problems in the Chebyshev method. I have made two improvements to the numerical efficiency of REM modelling of CSEM data. First, I develop a workflow to solve the 3D electric field by REM but with a 2D model. If the earth model can be simplified to 2D structures, the computational cost to achieve a 3D solution can be reduced by an order of magnitude. Secondly, the code has been parallelized by graphic processing units (GPU), and the performance can be improved by a factor of over 100, compared with the serial REM code implemented in C. The developed new functionalities make the REM algorithm an accurate forward modeller that solves the time-domain electric field efficiently in various environments. Subsequent CSEM inversion studies can therefore benefit from the method to extract resistivity model from full-bandwidth CSEM field data, which should bring us closer to the true subsurface

Technologies for Biomechanically-Informed Image Guidance of Laparoscopic Liver Surgery

Laparoscopic surgery for liver resection has a number medical advantages over open surgery, but also comes with inherent technical challenges. The surgeon only has a very limited field of view through the imaging modalities routinely employed intra-operatively, laparoscopic video and ultrasound, and the pneumoperitoneum required to create the operating space and gaining access to the organ can significantly deform and displace the liver from its pre-operative configuration. This can make relating what is visible intra-operatively to the pre-operative plan and inferring the location of sub-surface anatomy a very challenging task. Image guidance systems can help overcome these challenges by updating the pre-operative plan to the situation in theatre and visualising it in relation to the position of surgical instruments. In this thesis, I present a series of contributions to a biomechanically-informed image-guidance system made during my PhD. The most recent one is work on a pipeline for the estimation of the post-insufflation configuration of the liver by means of an algorithm that uses a database of segmented training images of patient abdomens where the post-insufflation configuration of the liver is known. The pipeline comprises an algorithm for inter and intra-subject registration of liver meshes by means of non-rigid spectral point-correspondence finding. My other contributions are more fundamental and less application specific, and are all contained and made available to the public in the NiftySim open-source finite element modelling package. Two of my contributions to NiftySim are of particular interest with regards to image guidance of laparoscopic liver surgery: 1) a novel general purpose contact modelling algorithm that can be used to simulate contact interactions between, e.g., the liver and surrounding anatomy; 2) membrane and shell elements that can be used to, e.g., simulate the Glisson capsule that has been shown to significantly influence the organ’s measured stiffness