# Mahadevan Ganesh

###### Professor, Applied Mathematics and Statistics

Professor, Computer Science

Affiliate Professor, Electrical Engineering

### Contact

### Research

- Stochastic, model reduction and multiscle algorithms
- Quantification of uncertainties in parallel scientific computing models
- Computational electromagnetics & High-performance computing
- High-order, high-performance computing algorithms for wave propagation and absorption simulations in 3-D.
- Forward and inverse acoustic and electromagnetic scattering in 3-D.
- Efficient algorithms for the Stokes and Navier-Stokes equations on rotating surfaces.
- Quadrature finite element methods for elliptic, parabolic and hyperbolic problems.
- Free surface nonlinear evolutionary systems with applications.
- Constructive approximations on spherical surfaces.
- Fully discrete spectral boundary integral and boundary element methods.
- Parallel evolutionary computations and analysis.
- Radial basis functions based numerical schemes for PDEs.

### Publications

- A fully discrete Galerkin method for high frequency exterior acoustic scattering in three dimensions .

(With S. C. Hawkins .) J. Comp. Phys. , 230 (2011), 104-125. - An efficient algorithm for simulating scattering by a large number of two dimensional particles.

(With S. C. Hawkins .) Aust. & NZ Indus. Appl. Math. (ANZIAM) J., 52 (2011), C139-C155. - A pseudospectral quadrature method for Navier-Stokes equations on rotating spheres

(With Q. T. Le Gia and I. H. Sloan .) Math. Comp. , 80 (2011), 1397-1430. - A radial basis Galerkin method for spherical surface Stokes equations.

(With Q.T. Le Gia .) Aust. & NZ Indus. Appl. Math. (ANZIAM) J., 52 (2011), C58-C71. - Convergence analysis with parameter estimates for a reduced basis acoustics scattering T-matrix method

(With S. C. Hawkins and R. Hiptmair .) IMA J. Numer. Anal., 32 (2012), 1348-1374. - A reduced basis method for electromagnetic scatttering by multiple particles in three dimensions

(With J. Hesthaven and B. Stamm .) J. Comput. Phys., 231 (2012), 7756-7779 - A stochastic pseudospectral and T-matrix algorithm for acoustic scattering by a class of multiple particle configurations

(With S. C. Hawkins .) J. Quant. Spect. Radiative Transfer, 123 (2013), 41-52 - Interpolation and cubature approximation and analysis for a class of wideband integrals on the sphere

(With V. Dominguez .) Advances in Comput. Math., 39, 547-584, 2013. - An efficient algorithm for simulation of stochastic scattering cross-sections

(With S. C. Hawkins .) Aust. & NZ Indus. Appl. Math. (ANZIAM) J., 54 (2013), C119-C136. - An all-frequency weakly-singular surface integral equation for electromagnetism in dielectric media: Reformulation and well-posedness analysis

(With S. C. Hawkins and D. Volkov .) J. Math. Anal. & Appl., 412 (2014), 277-300. - Spectral properties of Schrodinger operators on superconducting surfaces

(With T. Thompson .) J. Spectral Theory, 4 (2014), 569-612. - An efficient O(N) algorithm for computing O(N^2) acoustic wave interactions in large N-obstacle three dimensional configurations

(With S. C. Hawkins .) BIT Numer. Math., 55(2015), 117-139. - Schrodinger eigenbasis on a class of superconducting surfaces : Ansatz, analysis, FEM approximations and computations

(With T. Thompson .) Appl. Numer. Math., 89 (2015), 45-75. - A high performance computing and sensitivity analysis algorithm for stochastic many-particle wave scattering

(With S. C. Hawkins .) SIAM J Scientific Computing, 37 (2015), A1475-A1503 - Sobolev estimates for constructive uniform-grid FFT interpolatory approximations of spherical functions

(With V. Dominguez .) Advances in Comput. Math., 42 (2016), 843-887. - Scattering by stochastic boundaries: hybrid low- and high-order quantification algorithms

(With S. C. Hawkins .) Aust. & NZ Indus. Appl. Math. (ANZIAM) J., 56 (2016) C312-C338. - High-order FEM-BEM computer models for wave propagation in unbounded and heterogeneous media: Application to time-harmonic acoustic horn problem

(With C. Morgenstern .) J. Comp. Appl. Math., 307 (2016) 183-203. - An offline/online algorithm for a class of stochastic multiple obstacle configurations in half-plane.

(With S. C. Hawkins .) ) J. Comp. Appl. Math., 307 (2016) 52-64. - Parallel mixed FEM simulation of a class of single-phase models with non-local operators

(With A. Alyoubi .) J. Comp. Appl. Math., 307 (2016)106-118. - An efficient multigrid algorithm for heterogeneous acoustic media sign-indefinite high-order FEM model

(With C. Morgenstern .) Numer. Linear Algebra, 2017 (to appear, DOI: 10.1002/nla.2049). - Computing spatial correlation of ground motion intensities for shakeMap

(With S. A. Verros, D. J. Wald, C. B. Worden, M. Hearne .) Computers & Geosciences, 37:106-118, 2017). - TMATROM: A T-matrix Reduced Order Model Software

(With S. C. Hawkins .) ACM Trans. Math. Software, 2017 (to appear). - Sign-definite preconditioned high-order FEM. Part 1: Formulation and simulation for acoustic wave propagation in bounded homogeneous media.

(With C. Morgenstern .) SIAM J Scientific Computing, 2017 (to appear). - A spectrally accurate algorithm and analysis for a Ginzburg-Landau model on superconducting surfaces

(With T. Thompson .) SIAM J. Multiscale Model. Simul., 2017 (to appear). - High-order FEM domain decomposition models for high-frequency wave propagation in heterogeneous media.

(With C. Morgenstern S .) Submitted. - An FEM-MLMC algorithm for a moving shutter diffraction in time stochastic model.

(With B. Reyes and A. Purkayastha .) Submitted.

### Recent Courses

- MATH 440/540 Parallel Scientific Computing.
- BELS/MATH 433 Mathematical Biology.
- MATH 550 Numerical Methods for Partial Differential Equations.
- MATH 332/342 Linear Algebra.
- MATH 307 Introduction to Scientific Computing.