PhD in Numerical Analysis of PDEs - Monash University

Project Description

A PhD thesis is available to work on the design, analysis, and implementation of new mixed finite element methods for interface problems involving fluid-structure interaction in porous composite materials.

Special interest will be placed on studying the mathematical properties of the coupled PDE systems (solvability and regularity of weak solutions). In addition, the project focuses on the definition and testing of methods that can handle large amounts of data in an efficient manner and at the same time preserve the physically relevant principles satisfied by the equations they approximate (such as mass conservation). Further goals are the stability of the finite-dimensional problems associated with the discretisation via mixed finite elements and the convergence of approximate solutions.

Difficulties arise when the problem at hand is of a multiphysics nature (when a number of particular systems are interrelated and their solutions exhibit complex interdependencies); of a multiscale character (the processes take place at very different spatio-temporal scales); when it features high gradients in the model parameters (describing sharp interfaces between e.g. different material properties); or if non-equilibrium effects are present. Under such conditions, traditional approaches fail to be reliable and novel computational and mathematical techniques need to be explored. In this project the aim is to adapt and extend state-of-the-art methods to also accommodate the analysis of models including large deformations, non-trivial transmission conditions (contact, sliding, etc), and multi-species transport.

This type of problems are encountered in numerous phenomena in material sciences (characterisation of performance in photovoltaic devices), the mining industry (sedimentation of polydisperse suspensions interacting with rake mechanisms), and biomedical applications (perfusion of soft living tissues). It is expected that, apart from the PDE, numerical analysis, and scientific computing aspects of the project, the student is actively engaged in the applicative portions of the research.

Entry requirements

We are looking for candidates with academic excellence as well as having motivated to work on applied problems using sophisticate numerical methods for nonlinear and coupled PDEs. Applicants must have
* A Master degree (or equivalent) in mathematics;
* A solid background in PDEs and finite element methods;
* Some programming experience using, e.g., Python or C++;
* Provable strong oral and written communication skills in English.

How to apply

Candidates are invited to contact, providing their academic record, to know whether they satisfy the 1st class honours equivalence (which is a requirement for eligibility at Monash).

Informal inquiries can be then forwarded to A/Prof Ricardo Ruiz Baier with the subject "Inquiries - PhD Interfaces", and the application process requires to include a motivation letter, and a CV with detailed academic record and two references.

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Contact and application information
Sunday, July 5, 2020
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Graduate student fellowships