Research

My research interests are mainly in applied mathematics and computational science. These interests include the theoretical and computational aspects of numerical analysis, spectral theory, and partial differential equations, as well as mathematical modelling and collaborative work across different fields. Check out my Google Scholar profile for a list of my pre-prints and published research. A list of past and current research projects is given below.

Action potential under symptoms of LQT1 syndrome, and results after treatment (beta blockers). See full details here.

Numerical simulations in cardiac electrophysiology

We are currently studying the extracellular-membrane-intracellular (EMI) model and its applications in cardiac electrophysiology. Check out the project's page on ResearchGate to see the publications of this project.

Deformation of the gastrocnemius muscle during active contraction. See full pre-print here.

Modelling of skeletal muscles

We investigate the force and work output of muscle tissues based on numerical simulations. The finite element method is used in a 3D implementation of a dynamic problem in nonlinear elasticity. Check out the project's page on ResearchGate to see the publications of this project.

x-component of the 4th Jones eigenfunction on the unit square. See full details in this SIAM article or the pre-print version here.

Eigenvalue problems in linear elasticity

We study theoretical and numerical aspects of eigenproblems arising in linear elasticity. Check out the project's page on ResearchGate to see the publications of this project.

Optimization of the spectra

We numerically study local and global optimisers of the spectra of elliptic operators as a function of the shape of the domain where they are defined. Check out the project's page on ResearchGate to see the publications of this project.

Finite element approximation in Fluid mechanics

We study the stability and consistency of finite element approximations of problems in fluid mechanics. Check out the project's page on ResearchGate to see the publications of this project.

COLLABORATION

I have collaborated with the following researchers and students:

Raymond J. Spiteri, Professor at the University of Saskatchewan, Canada
Kevin R. Green, Research scientist at the University of Saskatchewan, Canada
Joyce Reimer, MSc student at the University of Saskatchewan, Canada
Reza Zolfaghari, Software developer at Altair, Canada

Nilima Nigam, Professor at Simon Fraser University, Canada
James M. Wakeling, Professor at Simon Fraser University, Canada
Jeffrey Ovall, Professor at Portland State University, USA
Jiguang Sun, Professor at Michigan Technological University, USA
Bobak Shahriari, Research scientist at Deep Mind, UK
David S. Ryan, Postdoctoral fellow at UC Riverside, USA
Stephanie A. Ross, Postdoctoral fellow at the University of British Columbia, Canada
Bart Bolsterlee, Postdoctoral fellow at NeuRA, Australia
Ryan Konno, MSc student at Simon Fraser University, Canada
Gabriel N. Gatica, Professor at Universidad de Concepcion, Chile
Salim Meddahi, Professor at Universidad de Oviedo, Spain
Antonio Marquez, Professor at Universidad de Oviedo, Spain

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