CAAM Faculty Publications

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 diagonal-norm 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 ...
• Multi-patch discontinuous Galerkin isogeometric analysis for wave propagation: Explicit time-stepping and efficient mass matrix inversion ﻿

(2018)
We present a class of spline finite element methods for time-domain wave propagation which are particularly amenable to explicit time-stepping. The proposed methods utilize a discontinuous Galerkin discretization to enforce ...
• Topological Schemas of Memory Spaces ﻿

(2018)
Hippocampal cognitive map-a neuronal representation of the spatial environment-is widely discussed in the computational neuroscience literature for decades. However, more recent studies point out that hippocampus plays a ...
• 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 solid-state phase transitions. These transitions modulate thermal and material fluxes across the mantle and variations in their ...
• Reduced order modeling for time-dependent optimization problems with initial value controls ﻿

(2018)
This paper presents a new reduced order model (ROM) Hessian approximation for linear-quadratic 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 small-angle dominated Coulomb collisions in fusion plasmas. We investigate a high order accurate, fully conservative, finite element discretization of the nonlinear ...
• A discrepancy-based 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 ...
• A Distributed-Memory Randomized Structured Multifrontal Method for Sparse Direct Solutions ﻿

(2017)
We design a distributed-memory randomized structured multifrontal solver for large sparse matrices. Two layers of hierarchical tree parallelism are used. A sequence of innovative parallel methods are developed for randomized ...
• An alternating direction and projection algorithm for structure-enforced matrix factorization ﻿

(2017)
Structure-enforced matrix factorization (SeMF) represents a large class of mathematical models appearing in various forms of principal component analysis, sparse coding, dictionary learning and other machine learning ...
• Angola Cameia Development Casing-Settlement Calculations ﻿

(2017)
The amount of axial settlement of casings supported by regions of axial elastic foundations is computed. The differential equation of axial equilibrium, including the foundation stiffnesses, is solved by use of cubic axial ...
• Full-waveform inversion via source-receiver extension ﻿

(2017)
Full-waveform inversion produces highly resolved images of the subsurface and quantitative estimation of seismic wave velocity, provided that its initial model is kinematically accurate at the longest data wavelengths. If ...
• Impact of Optimized Breastfeeding on the Costs of Necrotizing Enterocolitis in Extremely Low Birthweight Infants ﻿

(2016)
Objective: To estimate risk of necrotizing enterocolitis (NEC) for extremely low birth weight (ELBW) infants as a function of preterm formula (PF) and maternal milk intake and calculate the impact of suboptimal feeding on ...
• Shape Optimization of Shell Structure Acoustics ﻿

(2017)
This paper provides a rigorous framework for the numerical solution of shape optimization problems in shell structure acoustics using a reference-domain approach. The structure is modeled with Naghdi shell equations, fully ...
• A Branch Decomposition Algorithm for the p-Median Problem ﻿

(2017)
In this paper, we use a branch decomposition technique to improve approximations to the p-median problem. Starting from a support graph produced either by a combination of heuristics or by linear programming, we use dynamic ...
• Residual-Based Adaptivity and PWDG Methods for the Helmholtz Equation ﻿

(2015)
We present a study of two residual a posteriori error indicators for the plane wave discontinuous Galerkin (PWDG) method for the Helmholtz equation. In particular, we study the $h$-version of PWDG in which the number of ...
• A Comparison of High Order Interpolation Nodes for the Pyramid ﻿

(2015)
The use of pyramid elements is crucial to the construction of efficient hex-dominant meshes [M. Bergot, G. Cohen, and M. Duruflé, J. Sci. Comput., 42 (2010), pp. 345--381]. For conforming nodal finite element methods with ...