A5000005323- Advanced Numerical Methods in Computational Mathematics
- Optical Imaging and Spectroscopy Techniques
- Computational Geometry and Mesh Generation
- Photoacoustic and Ultrasonic Imaging
- Electromagnetic Simulation and Numerical Methods
- Scientific Computing and Data Management
- High-pressure geophysics and materials
- Geomagnetism and Paleomagnetism Studies
- Reservoir Engineering and Simulation Methods
- Distributed and Parallel Computing Systems
- earthquake and tectonic studies
- Advanced Mathematical Modeling in Engineering
- Computational Fluid Dynamics and Aerodynamics
- Numerical methods in inverse problems
- Geological and Geochemical Analysis
- Geological formations and processes
- Gaussian Processes and Bayesian Inference
- Hydrocarbon exploration and reservoir analysis
- Numerical methods in engineering
- Hydraulic Fracturing and Reservoir Analysis
- Parallel Computing and Optimization Techniques
- Lattice Boltzmann Simulation Studies
- Landslides and related hazards
- Numerical methods for differential equations
- Contact Mechanics and Variational Inequalities
Colorado State University
2017-2025
Collins College
2020
Mitchell Institute
2006-2019
Texas A&M University
2007-2016
Clemson University
2015
University of Victoria
2012
The University of Texas at Austin
2003-2006
St. Anthony Hospital
2005
Heidelberg University
2001
An overview of the software design and data abstraction decisions chosen for deal.II, a general purpose finite element library written in C++, is given. The uses advanced object-oriented encapsulation techniques to break implementations into smaller blocks that can be arranged fit users requirements. Through this approach, deal.II supports large number different applications covering wide range scientific areas, programming methodologies, application-specific algorithms, without imposing...
Numerical simulation of the processes in Earth's mantle is a key piece understanding its dynamics, composition, history and interaction with lithosphere core. However, doing so presents many practical difficulties related to numerical methods that can accurately represent these at relevant scales. This paper an overview state art algorithms for high-Rayleigh number flows such as those mantle, discusses their implementation Open Source code Aspect (Advanced Solver Problems ConvecTion)....
Computations have helped elucidate the dynamics of Earth's mantle for several decades already. The numerical methods that underlie these simulations greatly evolved within this time span, and today include dynamically changing adaptively refined meshes, sophisticated efficient solvers, parallelization to large clusters computers. At same time, many -- discussed in detail a previous paper series were developed tested primarily using model problems lack complexities are common realistic models...
Abstract This paper provides an overview of the new features finite element library deal.II version 8.4.
Abstract This paper provides an overview of the new features finite element library deal.II version 9.0.
Abstract This paper provides an overview of the new features finite element library deal.II, version 9.2.
Abstract This paper provides an overview of the new features finite element library deal.II, version 9.3.
Abstract This paper provides an overview of the new features finite element library deal.II, version 9.4.
Abstract This paper provides an overview of the new features finite element library deal.II , version 9.5.
Abstract This paper provides an overview of the new features finite element library deal.II, version 9.6.
Today's largest supercomputers have 100,000s of processor cores and offer the potential to solve partial differential equations discretized by billions unknowns. However, complexity scaling such large machines problem sizes has so far prevented emergence generic software libraries that support computations, although these would lower threshold entry enable many more applications benefit from large-scale computing. We are concerned with providing this functionality for mesh-adaptive finite...
Abstract This paper provides an overview of the new features finite element library deal.II version 8.5.
Abstract This paper provides an overview of the new features finite element library deal.II, version 9.1.
A three-dimensional fluorescence-enhanced optical tomography scheme based upon an adaptive finite element formulation is developed and employed to reconstruct fluorescent targets in turbid media from frequency-domain measurements made reflectance geometry using area excitation illumination. The algorithm derived within a Lagrangian framework by treating the photon diffusion model as constraint optimization problem. Adaptively refined meshes are used separately discretize maps of...
Optical tomography attempts to determine a spatially variable coefficient in the interior of body from measurements light fluxes at boundary. Like many other applications biomedical imaging, computing solutions optical is complicated by fact that one wants identify an unknown number relatively small irregularities this locations, for example corresponding presence tumors. To recover them resolution needed clinical practice, has use meshes that, if uniformly fine, would lead intractably large...
Abstract This paper gives an overview of adaptive discretization methods for linear second-order hyperbolic problems such as the acoustic or elastic wave equation. The emphasis is on Galerkin-type spatial well temporal discretization, which also include variants Crank-Nicolson and Newmark finite difference schemes. choice space time meshes follows principle \goaloriented" adaptivity based a posteriori error estimation employing solutions auxiliary dual problems.
Finite element methods approximate solutions of partial differential equations by restricting the problem to a finite dimensional function space. In hp adaptive methods, one defines these discrete spaces choosing different polynomial degrees for shape functions defined on locally refined mesh. Although this basic idea is quite simple, its implementation in algorithms and data structures challenging. It has apparently not been documented literature most general form. Rather, existing...
Many problems in geodynamic modelling result a non-linear Stokes problem which the viscosity depends on strain rate and pressure (in addition to other variables). After discretization, resulting system is most commonly solved using Picard fixed-point iteration. However, it well understood that Newton's method – when augmented by globalization strategies ensure convergence even from points far solution can be substantially more efficient accurate than solver. In this contribution, we evaluate...
Abstract. Geodynamical simulations over the past decades have widely been built on quadrilateral and hexahedral finite elements. For discretization of key Stokes equation describing slow, viscous flow, most codes use either unstable Q1×P0 element, a stabilized version equal-order Q1×Q1 or more recently stable Taylor–Hood element with continuous (Q2×Q1) discontinuous (Q2×P-1) pressure. However, it is not clear which these choices actually best at accurately simulating “typical” geodynamic...
This article describes a novel non-contact fluorescence optical tomography scheme which utilizes multiple area illumination patterns, to reduce the ill-posedness of inverse problem involved in recovering interior yield distributions biological tissue from boundary measurements. The image reconstruction is posed as an optimization seeks property distribution minimizing, for all patterns simultaneously, regularized difference between observed measurements light distribution, and predicted...