A5061716464- Advanced Numerical Methods in Computational Mathematics
- Computational Fluid Dynamics and Aerodynamics
- Fluid Dynamics and Turbulent Flows
- Electromagnetic Simulation and Numerical Methods
- Numerical methods for differential equations
- Numerical methods in engineering
- Model Reduction and Neural Networks
- Differential Equations and Numerical Methods
- Meteorological Phenomena and Simulations
- Fractional Differential Equations Solutions
- Navier-Stokes equation solutions
- Stability and Controllability of Differential Equations
- Seismic Imaging and Inversion Techniques
- Gas Dynamics and Kinetic Theory
- Lattice Boltzmann Simulation Studies
- Numerical methods in inverse problems
- Advanced Numerical Analysis Techniques
- Electromagnetic Scattering and Analysis
- AI in cancer detection
- Seismic Waves and Analysis
- Geophysical Methods and Applications
- Matrix Theory and Algorithms
- Photoacoustic and Ultrasonic Imaging
- Breast Lesions and Carcinomas
- Nonlinear Dynamics and Pattern Formation
University of Waterloo
2022-2024
National Institute of Aerospace
2017-2022
Langley Research Center
2017-2022
University of Toronto
2013-2017
Western University
2010
Robarts Clinical Trials
2008-2009
Summation-by-parts (SBP) finite-difference discretizations share many attractive properties with Galerkin finite-element methods (FEMs), including time stability and superconvergent functionals; however, unlike FEMs, SBP operators are not completely determined by a basis, so the potential exists to tailor meet different objectives. To date, application of high-order multiple dimensions has been limited tensor product domains. This paper presents definition for multidimensional that is...
The construction of high order entropy stable collocation schemes on quadrilateral and hexahedral elements has relied the use Gauss--Legendre--Lobatto points their equivalence with summation-by-parts (SBP) finite difference operators. In this work, we show how to efficiently generalize semidiscretely tensor product Gauss generalized SBP Numerical experiments suggest that significantly improves accuracy curved meshes.
Freehand ultrasound-guided breast biopsy may present difficulties in needle visualization within the scanning plane of ultrasound image. Scanning and misalignment, an unknown insertion site (relative to image), trajectory before insertion, physician experience play roles difficulty these procedures. The objective our study was compare currently used freehand technique with use a guidance system that limits motion for biopsy.We developed is composed electronically tracked passive mechanical...
Image-guided needle biopsies are currently used to provide a definitive diagnosis of breast cancer; however, difficulties in tumor targeting exist as the ultrasound (US) scan plane and biopsy must remain coplanar throughout procedure display actual tip position. The additional time associated with aligning maintaining this relationship results increased patient discomfort. Biopsy procedural efficiency is further hindered since pathway interpretation often difficult, especially for insertions...
The generalization of summation-by-parts operators for the first derivative Del Rey Fernández, Boom, and Zingg [J. Comput. Phys., 266 (2014), pp. 214--239] is extended to approximations second derivatives with a constant or variable coefficient. This enables construction second-derivative one more following characteristics: (i) nonrepeating interior point operators, (ii) nonuniform nodal distributions, (iii) exclusion both boundary nodes. Definitions are proposed that give rise generalized...
The entropy conservative/stable algorithm of Friedrich~\etal (2018) for hyperbolic conservation laws on nonconforming p-refined/coarsened Cartesian grids, is extended to curvilinear grids the compressible Euler equations. primary focus constructing appropriate coupling procedures across interfaces. A simple and flexible approach proposed that uses interpolation operators from one element other. On faces, analytic metrics are used construct terms, while metric terms in volume approximated...