Electromagnetics Research Group-Applied Computational Electroscience
Shanker Balasubramaniam | bshanker@egr.msu.edu | www.egr.msu.edu/~bshanker
Research in the Applied Computational Electroscience (ACES) Laboratory includes computational electromagnetics; frequency and time domain integral equation–based methods; multi-scale fast multipole methods, fast transient methods, parallel algorithms; higher order finite element and integral equation methods; ISOgeometric analysis, propagation in complex media; mesoscale electromagnetics; particle and molecular dynamics as applied to multiphysics and multiscale problems.
Developing mathematically rigorous, novel computational methods with provable algorithmic efficiency to solve a range of problems in electroscience is the focus of the ACES group. This pursuit relies on advancing three inter-related areas: applied mathematics, applied physics, and computer science. In what follows, we shall briefly elucidate some of the recent advances made by our group.
Rapid evaluation of Green’s kernels for a number of different potentials
Integral equations based analysis methods play a critical role in solution of a number of physical systems ranging from molecular dynamics to astrophysics to electrostatics to electromagnetics. These systems are set up using the appropriate Green’s function, and the resulting cost and memory complexity. If time is involved, as in the wave equation or diffusion equation, the cost scales as O(Ntα Ns2), where Nt and Ns are the numbers of temporal and spatial degrees of freedom, and 0 ≤ α ≤ 2. Over the years, we have developed mathematically rigorous algorithms with provable error bounds that scale as O(Ns·logαNs) and O(Nt·logαNtNs·logαNs). These algorithms have been applied to a number of problems ranging from molecular dynamics to acoustics to electromagnetics. Provably scalable parallel algorithms for large multiscale analysis that rely on these methods have also been developed.
Isogeometric integral equation solvers and shape/topology optimization
Integral equation solvers form the backbone of analysis in both acoustics and electromagnetic scattering problems. Methods developed rely definition of physical quantities on piecewise continuous description of the domain. The state of art is dramatically different in computer graphics community where geometric descriptions with higher order of continuity abound. Using the same set of basis for both geometric description as well as defining physical quantities on these description has manifold advantages, from (i) seamless h-adaptivity to (ii) local refinement to (iii) morphing and (iv) shape/topology optimization.
Light-matter interaction
Rigorous quantum mechanical modeling of light-matter interaction is vital to the analysis of numerous processes, ranging from resonant energy transfer in light-harvesting/light-generation applications, to the generation and preservation of entanglement between qubits in quantum information applications. Here, quantum emitters such as molecules, optically active defects, or quantum dots can interact over large distances by way of their mutual coupling to the electromagnetic field. The nature of this second-order interaction is a complex function of the electromagnetic environment. Multiphysics solvers are being used to study Liouville equations describing the dynamics of quantum emitters coupled through the electromagnetic field, wherein the fi eld-mediated interaction parameters can be extracted from classical solutions to the Maxwell equations in realistic material environments. Ongoing work includes development of higher order transparent boundary conditions for the analysis of strong light-matter coupling in high-Q cavities, as well as cavity design and optimization for the generation of maximally entangled states.
Dynamics of microbubbles
Another intriguing problem that we have recently started investigating is understanding the dynamics of microbubbles. These find several applications ranging from imaging as an ultrasound contrast agent, micro- bubble to drug delivery to noninvasive therapy or even in genetic engineering. The fundamental problem is to accurately understand dynamics of microbubbles in the presence of ultrasound. We are actively investigating a series of problems of increasing complexity: single bubble motion, bubble deformation due to pressure, combined bubbles dynamics, and ultrasound steering, etc.
Other research
In addition to the aforementioned areas, we have pioneered the development of stable time domain integral equation solvers, a technology that remained an unsolved problem for more than four decades. We have recently made significant inroads into multiscale and multiphysics modeling of plasma-reactors, and accelerators that include electromagnetics, plasma physics, fluid flows, and heat transfer.
