Our preprint on Automated adjoints of coupled ODE-PDE systems is now available on arXiv! Mathematical models that couple partial differential equations (PDEs) and spatially distributed ordinary differential equations (ODEs) arise in biology, medicine, chemistry and many other fields. In this paper we present extension to the FEniCS and dolfin-adjoint softwares for expressing and efficiently solving such coupled systems. Given an ODE described using an augmentation of the Unified Form Language (UFL) and a discretisation described by an arbitrary Butcher tableau, efficient code is automatically generated for the parallel solution of the ODE. The high-level description of the solution algorithm also facilitates the automatic derivation of the adjoint and tangent linearization of coupled PDE-ODE solvers. The supplementary code for the paper is also openly available.
I am happy to announce that Dr. Travis Thompson joined the Waterscape project as a postdoctoral fellow at Simula Research Laboratory on June 8 2017. Travis received a PhD in Mathematics from Texas A&M university in 2013; his research areas are numerical analysis, and scientific computing. Recently published work is focused on the construction of a-priori error estimates, and solver development, for finite element methods applied to problems in computational fluid dynamics, and biomechanics. Within Waterscape, Travis will be studying a-priori and a-posteriori error analysis of mixed finite element methods for generalized poroelasticity aiming at accurate, robust and property-preserving methods.
Our short and sweet software paper on cbcbeat: an adjoint-enabled framework for computational cardiac electrophysiology by Rognes, Farrell, Funke, Hake and Maleckar has been accepted and published in the Journal of Open Source Software: http://joss.theoj.org/papers/8403a4b6cabff51d99d6b0a433358016
Late last year, I received an email from a member of the TEDxOslo organization committee, asking if I would be interested in giving a TEDx talk at TEDxOslo 2017 taking place in the National Theatre on May 3 2017. Enjoy the end result here:
I am truly grateful and honoured that the European Research Council has awarded me with a 5-year Starting Grant within Mathematics (PE1) to fund the Waterscales project, a project dedicated to the mathematical and computational foundations for modeling cerebral fluid flow.
The Waterscales vision
Over the next decades, mathematics and numerics could play a crucial role in gaining new insight into the mechanisms driving water transport through the brain. Indeed, medical doctors express an urgent need for multiscale modeling and simulation – to overcome fundamental limitations in traditional techniques. Surprisingly little attention has been paid to the numerics of the brain’s waterscape however, in stark contrast to the role of simulation in other fields of neuroscience, and key mathematical models and methods are missing. To address this important challenge, the overall ambition of the Waterscales project is to establish the mathematical, numerical and computational foundations for predictively modeling fluid flow and solute transport through the brain across spatiotemporal scales – from the cellular to the organ level.