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Space-Time Hexahedral Finite Element Methods for Parabolic Evolution Problems
Time-step** methods in combination with some spatial discretization method like the finite element method (FEM) are still the standard approach to...
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The Equations of Magnetohydrodynamics
In this chapter, a summary of electromagnetics and fluid mechanics equations from physics and mathematical perspectives is provided for the case of...
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Longitudinal Harmonization for Improving Tractography in Baby Diffusion MRI
The human brain develops very rapidly in the first years of life, resulting in significant changes in water diffusion anisotropy. Developmental...
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Riemann-DTI Geodesic Tractography Revisited
Clinical tractography is a challenging problem in diffusion tensor imaging (DTI) due to persistent validation issues. Geodesic tractography, based on...
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Spectral Analysis of Continuous FEM for Hyperbolic PDEs: Influence of Approximation, Stabilization, and Time-Step**
We study continuous finite element dicretizations for one dimensional hyperbolic partial differential equations. The main contribution of the paper...
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Stochastic Gauss–Newton Algorithms for Online PCA
In this paper, we propose a stochastic Gauss–Newton (SGN) algorithm to study the online principal component analysis (OPCA) problem, which is...
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A Compact Difference Scheme on Graded Meshes for the Nonlinear Fractional Integro-differential Equation with Non-smooth Solutions
In this paper, a compact finite difference scheme for the nonlinear fractional integro-differential equation with weak singularity at the initial...
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A numerical investigation of CO2 dilution on the thermochemical characteristics of a swirl stabilized diffusion flame
The turbulent combustion flow modeling is performed to study the effects of CO 2 addition to the fuel and oxidizer streams on the thermochemical...
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Construction of Entropy Conservative Flux Reconstruction Schemes on Arbitrary Meshes
After having proposed a new linear stable DG discretization, we focus again on flux reconstruction methods. We have introduced these methods in...
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High-order weighted compact nonlinear scheme for solving degenerate parabolic equations
Solutions of the nonlinear degenerate parabolic equations may be discontinuous. The classical numerical schemes cannot well handle such...
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Spatial Sparse Estimation of Fiber Orientation Distribution Using Deep Alternating Directions Method of Multipliers Network
Sparse prior information is introduced to improve the accuracy ofFiber direction distribution (FOD) estimation. Spatial continuity is another...
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Obtaining Representative Core Streamlines for White Matter Tractometry of the Human Brain
Diffusion MRIDiffusion MRI infers information about the micro-structural architecture of the brain by probing the diffusion of water molecules. The...
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Overview of the AFT Model for Transition Prediction in Complex Aerodynamic Flows
For many aerodynamic flows of practical interest, prediction of laminar-turbulent transition from first principles is a difficult, if not impossible,...
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A Shock Stabilization of the HLLC Riemann Solver for the Carbuncle Instability
The HLLC approximate Riemann solver improves upon the HLL Riemann solver by resolving contact discontinuities. This is a particularly desirable...
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Electroosmotic Peristaltic Pum** of Jeffrey Liquid with Variable Characteristics: An Application to Hemodynamic
The current model investigates the electroosmotic characteristics of the Jeffrey fluid's peristaltic transport in a uniform channel to study the...
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Heart Valve Computational Flow Analysis with Boundary Layer and Leaflet Contact Representation
We present an overview our computational framework for heart valve flow analysis with boundary layer and leaflet contact representation. The...
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A three-step defect-correction stabilized algorithm for incompressible flows with non-homogeneous Dirichlet boundary conditions
Based on two-grid discretizations and quadratic equal-order finite elements for the velocity and pressure approximations, we develop a three-step...
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Diffusion MRI Outside the Brain
ThisDiffusion manuscript provides an overview of recent developments inDiffusion Diffusion-Weighted Imaging (DWI) outside the brain, focusing on...
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Optimal stop** and impulse control in the presence of an anticipated regime switch
We consider a class of stochastic optimal stop** and impulse control problems where the agent solving the problem anticipates that a regime switch...