A GPU Computing Engine: State-of-the-art Parallelizable Numerical Methods for Simulation of Complex Multi-Scale Systems


Since first published in 1949, the Monte-Carlo method has been a prominent technique for tackling the simulation of complex physical systems by solving the underlying multi-dimensional integration and boundary-value problem using random number generation. Numerical solutions based on implicit techniques (finite difference and finite element methods) have been widely adopted for solving boundary-value problems in physical domains, although some inherent shortcomings in these methods made them impractical in several important applications, in particular when meshing large domains or when modeling multi-scale systems. Implicit techniques place a high demand in computational hardware requirements (memory size and computing power) when complex geometries are analyzed, making the simulation time prohibitive when modeling certain systems, such as heat conduction problems with abrupt changes in thermal diffusivity, as present at cryogenic systems with composite layered materials.

The computational bottleneck in implicit methods is given by the need to invert a large matrix, whose size grows with the number of elements in the model. The Monte-Carlo method uses the evolution of “particles” within the domain to solve the boundary value problem, using random number generation to solve the inherent multi-dimensional integration within the domain, thereby bypassing the need of inverting a large matrix. For decades, the practical advantages of using Monte Carlo methods as opposed to finite elements have been marginal or nil due to the available computing hardware, and finite element tools have grown to be a multi-billion dollar industry today. In recent years, however, a hardware and software technology breakthrough has taken place with the advent of GPU computing: powerful and relatively inexpensive massively parallel computing resources are now available, leading to a reassessment of the advantages of Monte Carlo methods over finite elements in problems where the shortcomings of implicit methods make simulation times impractical.

Reza Bahadori (PhD candidate) and Professor Hector Gutierrez at the Florida Institute of Technology, in collaboration with Dr. Shashikant Manikonda and Dr. Rainer Meinke from AML Superconductivity and Magnetics, Florida, have developed a novel approach for the simulation of three-dimensional transient conductive heat transfer from a homogeneous media to a non-homogeneous multi-layered composite material with temperature dependent thermal properties using a mesh-free Monte-Carlo method, published in the International Journal of Heat and Mass Transfer.

The proposed approach accounts for the impact of thermal diffusivities from source to sink in the calculation of the particles’ step length, and a derivation of the three-dimensional peripheral integration to account for the influence of material properties around the sink on its temperature. Then, a transient Bessel function solution is combined with a steady-state peripheral integral method to simulate the transient heat conduction in composite media with temperature dependent material properties. Simulations developed by the proposed approach were compared against both experimental measurements and results from a finite element simulation.

The proposed mesh-free method is well suited for modelling intricate geometries and multi-scale systems where solution by conventional finite element tools would require very large number of elements, leading to prohibitively long simulation times. The results were validated by both experimental measurements and finite element simulations, showing that accurate results using the Monte Carlo approach can be achieved with a relatively small number of “particles”.

The proposed approach holds great promise for simulation of multi-scale problems such as the multi-physics analysis of quench in superconducting magnets, where proper representation of superconducting tapes and insulation remains a significant challenge using conventional finite element tools. Solution to the first and second types of thermal boundary conditions have been developed and verified – the extension of the proposed approach to the third kind of boundary condition is currently under development.

About the author

Reza Bahadori is Ph.D. candidate of Mechanical Engineering at Florida Institute of Technology. Reza received his M.Sc. degree in Mechanical Engineering also from Florida Institute of Technology in 2015. His focus is computational mechanics for tackling complex problems in areas such as heat transfer, superconductivity and vibration. Part of his doctorate research proposes new solution for the Multi-dimensional transient heat conduction from a homogeneous medium to a non-homogeneous multi-layered composite material with temperature dependent thermal properties using a mesh-free and highly parallelizable method.

His achievements can be summarized in several journal publications related to vibration, heat transfer and application to quench simulation in superconductors, I-Corps and PFI NSF grants based on his Ph.D. research finalist of best paper student contest in IEEE conference and outstanding graduate student at Florida Institute of Technology.

About the author

Hector Gutierrez received the Ph.D. degree in Electrical Engineering in 1997 and the the M.Eng. Degree in Manufacturing Systems Engineering in 1993, from North Carolina State University. He received the B.Sc. Degree in Applied Mathematics from Universidad Cayetano Heredia, Lima, in 1989, and the B.Sc. in Mechanical Engineering from the Pontificia Universidad Catolica del Peru in 1991. He has been with the Department of Mechanical & Aerospace Engineering, Florida Institute of Technology since 1999, where he is currently a Professor.

His professional interests are in automatic control and mechatronics for aerospace systems, motion control, and flexible structures. He received the National Science Foundation CAREER Award in 2001 and the Office of Naval Research Young Investigator Award in 2003, both for his work in magnetic suspension systems.

About the author

Dr. Rainer Meinke is an international expert in the science and application of superconductivity and advanced magnetics. With over two decades of experience in superconducting magnet design and testing for major science projects, Dr. Meinke co-founded and has led the company’s technical developments, which has culminated in a radical new end-to-end process for magnet design and manufacturing that yields magnets with virtually perfect fields. His strategic achievements include a rich IP portfolio, including AML CoilCADTM, the most sophisticated magnet design software ever devised, as well as dozens of breakthrough innovations such as the Double-HelixTM family of magnet technologies.

In a career in physics and engineering that spans more than 30 years, Dr. Meinke has led some of the world’s most advanced accelerator facilities. As Senior Scientist at the Superconducting Super Collider Laboratory (SSCL), in Dallas Texas, he was the Collider Machine Leader, and was responsible for technical design, budget and schedule of the 20 TeV proton-proton Collider. Previously, he led the development, build-up and operation of a test facility for superconducting magnets at HERA, in Hamburg, Germany–the first accelerator to employ industrially produced magnets of this kind.

His work in physics included development of phenomenological models for elementary particle interactions, and hardware development and experimental data analysis for high-energy physics experiments at different accelerators and laboratories, including construction of the world’s largest streamer chamber detector at the European Center for Nuclear Research (CERN).

Dr. Meinke has numerous patents related to superconducting systems and has authored over a 100 publications. His accomplishments in creating practical solutions for complex technical problems has been recognized throughout the science community, making him a frequent invited speaker and reviewer for international science conferences and journals. He received his Ph.D. in high-energy physics from Technical University in Munich, Germany

About the author

Dr. Shashikant Manikonda has received B.Sc. in Physics from Indian Institute of Technology, Kharagpur in 2000 and Ph.D in Physics from Michigan State University, East Lansing, MI in 2006. He worked as post-doctoral researcher and Accelerator Physicist at Argonne National Laboratory before joining AML Superconductivity and Magnetics, Palmbay, FL in 2012. In 2017 he started MagTech Solutions LLC, Melbourne, FL to provide technical consulting services. From 2001-2012 he has worked on large international collaborative projects dealing with design and construction of next generation particle accelerator systems in USA, Germany, Japan and France. At AML he worked on projects involving application of state-of-the-art superconducting magnet and permanent magnet technology for energy, medical, and space sectors. He has authored 30+ publications and was invited speaker at international conferences.


Reza Bahadori, Hector Gutierrez, Shashikant Manikonda, Rainer Meinke. A mesh-free Monte-Carlo method for simulation of three-dimensional transient heat conduction in a composite layered material with temperature dependent thermal properties.. International Journal of Heat and Mass Transfer, volume 119 (2018) page 533–541.

Go To International Journal of Heat and Mass Transfer

Check Also

jet impact speed in near-field electrospinning for precise patterning of nanofiber - Advances in Engineering

Researchers are reaching to the lower boundary of jet-speed in electrospinning to enable programmable microscale patterning of nanofibers