Computational and Applied Mathematics
Recent Submissions

An accelerated Poisson solver based on multidomain spectral discretization
(2018)This paper presents a numerical method for variable coefficient elliptic PDEs with mostly smooth solutions on two dimensional domains. The method works best for domains that can readily be mapped onto a rectangle, or a ... 
Weight‐adjusted discontinuous Galerkin methods: Matrix‐valued weights and elastic wave propagation in heterogeneous media
(2018)Weight‐adjusted inner products are easily invertible approximations to weighted L2 inner products. These approximations can be paired with a discontinuous Galerkin (DG) discretization to produce a time‐domain method for ... 
On discretely entropy conservative and entropy stable discontinuous Galerkin methods
(2018)High order methods based on diagonalnorm summation by parts operators can be shown to satisfy a discrete conservation or dissipation of entropy for nonlinear systems of hyperbolic PDEsﾠ[1],ﾠ[2]. These methods can also be ... 
Multipatch discontinuous Galerkin isogeometric analysis for wave propagation: Explicit timestepping and efficient mass matrix inversion
(2018)We present a class of spline finite element methods for timedomain wave propagation which are particularly amenable to explicit timestepping. The proposed methods utilize a discontinuous Galerkin discretization to enforce ... 
Topological Schemas of Memory Spaces
(2018)Hippocampal cognitive mapa neuronal representation of the spatial environmentis widely discussed in the computational neuroscience literature for decades. However, more recent studies point out that hippocampus plays a ... 
Discretization of Multipole Sources in a Finite Difference Setting for Wave Propagation Problems
(20180620)Seismic sources are commonly idealized as pointsources due to their small spatial extent relative to seismic wavelengths. The acoustic isotropic pointradiator is inadequate as a model of seismic wave generation for seismic ... 
Compositional heterogeneity near the base of the mantle transition zone beneath Hawaii
(2018)Global seismic discontinuities near 410 and 660 km depth in Earth’s mantle are expressions of solidstate phase transitions. These transitions modulate thermal and material fluxes across the mantle and variations in their ... 
Reduced order modeling for timedependent optimization problems with initial value controls
(2018)This paper presents a new reduced order model (ROM) Hessian approximation for linearquadratic optimal control problems where the optimal control is the initial value. Such problems arise in parameter identification and ... 
An exact redatuming procedure for the inverse boundary value problem for the wave equation
(2018)Redatuming is a data processing technique to transform measurements recorded in one acquisition geometry to an analogous data set corresponding to another acquisition geometry, for which there are no recorded measurements. ... 
Mapping Mantle Transition Zone Discontinuities Beneath the Central Pacific With Array Processing ofﾠSSﾠPrecursors
(2017)We image mantle transition zone (MTZ) discontinuities beneath the Central Pacific using ~120,000 broadband SS waveforms. With a wave packet‐based array processing technique (curvelet transform), we improve the signal‐to‐noise ... 
Landau Collision Integral Solver with Adaptive Mesh Refinement on Emerging Architectures
(2017)The Landau collision integral is an accurate model for the smallangle dominated Coulomb collisions in fusion plasmas. We investigate a high order accurate, fully conservative, finite element discretization of the nonlinear ... 
A discrepancybased penalty method for extended waveform inversion
(2017)Extended waveform inversion globalizes the convergence of seismic waveform inversion by adding nonphysical degrees of freedom to the model, thus permitting it to fit the data well throughout the inversion process. These ... 
Subset Selection and Feature Identification in the Electrocardiogram
(201804)Each feature in the electrocardiogram (ECG) corresponds to a different part of the cardiac cycle. Tracking changes in these features over long periods of time can offer insight regarding changes in a patient’s clinical ... 
Efficient estimation of coherent risk measures for riskaverse optimization problems governed by partial differential equations with random inputs
(201705)This thesis assesses and designs structureexploiting methods for the efficient estimation of risk measures of quantities of interest in the context of optimization of partial differential equations (PDEs) with random ... 
Analysis of inverse boundary value problems for elastic waves
(201804)In seismology, people use waves generated by earthquakes, artificial explosions, or even “noises”, to detect the Earth’s interior structure. The waves traveling in rocks, which are the main components of Earth’s crust and ... 
Graph Coloring, Zero Forcing, and Related Problems
(201705)This thesis investigates several problems related to classical and dynamic coloring of graphs, and enumeration of graph attributes. In the first part of the thesis, I present new efficient methods to compute the chromatic ... 
Nonlinear Waveform Inversion with SurfaceOriented Extended Modeling
(201703)This thesis investigates surfaceoriented model extension approach to nonlinear full waveform inversion (FWI). Conventional leastsquares (LS) approach is capable of reconstructing highly detailed models of subsurface. ... 
A ParallelInTime GradientType Method For Optimal Control Problems
(201705)This thesis proposes and analyzes a new parallelintime gradienttype method for timedependent optimal control problems. When the classical gradient method is applied to such problems, each iteration requires the forward ... 
An Inverse Free Projected Gradient Descent Method for the Generalized Eigenvalue Problem
(201705)The generalized eigenvalue problem is a fundamental numerical linear algebra problem whose applications are wide ranging. For truly largescale problems, matrices themselves are often not directly accessible, but their ... 
Novel Techniques for the ZeroForcing and pMedian Graph Location Problems
(201705)This thesis presents new methods for solving two graph location problems, the pMedian problem and the zeroforcing problem. For the pmedian problem, I present a branch decomposition based method that finds the best ...