Publications
Journal Publications
Causley, M.F. and Petropoulos, P.G. Efficient high-order methods for solving fractional differential equations of order $\alpha \in (0,1)$ using fast convolution and applications in wave propagation. in preparation.
Causley, M. The Gamma Function via Interpolation. Numerical Algorithms, vol. xx, no. x, pp. x-xx, 2021.
Seal, D. C. and Causley, M. On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science, vol. 14, no. 1, pp. 33-64, 2019. (Arxiv version).
Causley, M. and Morell, P. Sequences which converge to e: New insights from an old formula. General Mathematics, vol. 25, no. 2, pp. 159-173, 2017.
Causley, M., Cho, H. and Christlieb, A. Method of lines transpose: energy gradient flows using direct operator inversion for phase field models. SIAM Journal on Scientific Computing, vol. 39, no. 5, pp. B968-B992, 2017.
Causley, M.F., Christlieb, A., and Wolf, E. Method of lines transpose: an efficient unconditionally stable solver for wave propagation. Journal of Scientific Computing, vol. 70, no. 2, pp.896-921, 2017.
Bettencourt, M., Causley, M., Christlieb, A., and Wolf, E. A particle-in-cell method for the simulation of plasmas based on an unconditionally stable field solver. Journal of Computational Physics, vol. 326, no. 1, pp.324-372, 2016.
Causley, M.F. and Christlieb, A. Cho, H. and Seal, D. C. Method of lines transpose: High order L-stable O(N) schemes for parabolic equations using successive convolution. SIAM Journal on Numerical Analysis, vol. 54, no. 3, pp.1635-1652, 2016 (arxiv version).
Bradonjic, M. and Cohen, A. and Causley, M. F. Stochastic optimal control models for online seller under reputational mechanisms. Risks, vol. 3, no. 4, pp. 553-572, 2015.
Causley, M.F., Christlieb, A., Van Groningen, L. and Ong, B. Method of Lines Transpose: An Implicit Solution to the One Dimensional Wave Equation. Mathematics of Computation, vol. 83, no. 290, pp. 2763-2786, 2014.
Causley, M.F., and Christlieb, A. Higher order A-stable schemes for the wave equation using a successive convolution approach. SIAM Journal of Numerical Analysis, vol. 52, no. 1, pp. 220–235, 2014 (arxiv version).
Causley, M.F. and Petropoulos, P.G. On the Time-Domain Response of Havriliak-Negami Dielectrics. Transactions on Antennas and Propagation, vol. 61, no. 6, pp. 3182-3189, 2013.
Causley, M.F., Petropoulos, P.G. and Jiang, S. Incorporating the Havriliak-Negami Dielectric Model in the FD-TD Method. Journal of Computational Physics, vol. 230, no. 10, pp. 3884-3899, 2011.
McCartin, B.J. and Causley, M.F. Angled Derivative Approximation of the Hyperbolic Heat Conduction Equations, Journal of Applied Mathematics and Computation, vol. 182, pp. 1581-1607, 2006.
Dissertation
Asymptotic and numerical analysis of time-dependent wave propagation in dispersive dielectric media that exhibit fractional relaxation. New Jersey Institute of Technology, May, 2011.
Advisor: Peter G. Petropoulos
Workshop Proceedings
Kepler, G., Beavers, D., Battacharya, A., Causley, M., Chai, J., Holm, K. and Wanner, N. Problem 1: Cardiovascular events associated with oral and IV-administered antibacterial agents. Fourteenth Industrial Mathematical and Statistical Modeling (IMSM). July 21-29, 2008; Raleigh, North Carolina.
Presentations
Invited Presentations
Successive Convolution: a High Order Framework for PDEs Based on the Method of Lines Transpose. 2016 SIAM Annual Meeting. July, 2016. Boston, Massachusetts.
Resolvent Expansions for Higher-order Simulations of PDEs. SIAM CSE 2015. March 2015; Salt Lake City, Utah.
Stable, Accurate, and Efficient Schemes for Parabolic Problems using the Method of Lines Transpose. 2014 SIAM Annual Meeting. July 2014; Chicago, Illinois.
Higher Order O(N) schemes for hyperbolic problems using successive convolution. 2013 SIAM Conference on Analysis of Partial Differential Equations. December, 2013; Orlando, Florida.
Explicit A-stable schemes of higher order for the wave equation. New Jersey Institute of Technology. November, 2013; Newark, New Jersey.
Numerical methods for addressing multiple scales in plasma simulations. University of Michigan Dearborn. November, 2013; Dearborn, Michigan.
Higher order A-stable schemes for the wave equation through successive convolution. University of Michigan Flint. October, 2013; Flint, Michigan.
A Fast Implicit Maxwell Solver. Oak Ridge National Labs, June 2013; Oak Ridge, Tennessee.
Solving the Wave Equation in Plasmas Using the Method of Lines Transpose. Kettering University. April, 2013; Flint, Michigan.
Contributed Presentations
Perfectly Matched Layers for Wave Propagation: An Introduction. Kettering Mathematics Seminar. April 2016. Flint, MI.
Higher Order Methods for PDEs using Successive Convolution. 12th Annual Frontiers in Applied and Computational Mathematics (FACM). Newark, New Jersey. June, 2015.
Higher Order Methods for PDEs using Successive Convolution. SIAM Great Lakes Section Annual Conference. Grand Rapids, Michigan. May, 2015.
Higher Order A-Stable Schemes for the Wave Equation. International Conference on Applied Mathematics, Modeling and Computational Science (AMMCS 2013). August, 2013; Waterloo, Ontario, Canada.
An Implicit Maxwell Solver based on the Method of Lines Transpose. SIAM CSE 2013. February, 2013; Boston, Massachusetts.
A Novel Implicit Maxwell Solver. 39th International Conference on Plasma Science (ICOPS). July, 2012; Edinburgh, Scotland.
A Numerical Method for Simulating EM Wave Propagation in Dielectrics that Exhibit Fractional Relaxation. SIAM Annual Meeting. July, 2010; Pittsburgh, Pennsylvania.
The Frequency-dependent Havriliak-Negami Dielectric Permittivity Model. 7th Annual Frontiers in Applied and Computational Mathematics (FACM). May, 2010; Newark, New Jersey.
Stability and Error Analysis of the Cole-Cole Dielectric Model. SIAM Annual Meeting. July, 2009; Denver, Colorado.
Numerical Solution of the Hyperbolic Heat Conduction Equation by the Method of Angled Derivatives. Michigan Undergraduate Mathematics Conference. October, 2005; Flint, Michigan.
Poster Presentations
Poster. Presented at the Kettering Homecoming Poster Presentation, 2017.
Poster. Presented at the Kettering Homecoming Poster Presentation, 2017.
Poster. Presented at the Kettering Homecoming Poster Presentation, 2016.
Poster. Presented at the Kettering Homecoming Poster Presentation, 2016.
A Fast A-Stable Boundary Integral Solver for Maxwell's Equations. Presented at The combined 19th IEEE Pulsed Power Conference (PPC) and the 40th IEEE International Conference on Plasma Science (ICOPS). June, 2013; San Francisco, California.
A Novel Implicit Maxwell Solver. Presented at the 39th International Conference on Plasma Science (ICOPS). July, 2012; Edinburgh, Scotland.
Asymptotic Results for the Havriliak-Negami Dielectric Model. Presented at the 6th Annual Graduate Student Research Day. November, 2010; NJIT, Newark, New Jersey.
Numerical Analysis of the Cole-Cole Dielectric Model. Presented at the Dana Knox Student Research Showcase. April, 2009; NJIT, Newark, New Jersey.