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 Ms. Ada Ellingsrud joined the Waterscales project as a PhD candidate at Simula Research Laboratory on Aug 15 2017. Ada received a Masters degree in Applied Mathematics from the University of Oslo in 2015. Her thesis investigated preconditioning of unified mixed discretizations of the coupled Darcy-Stokes problem. Within Waterscales, Ada will be developing and studying multiscale models and methods for fluid flow and transport in brain tissue bridinging glial cell dynamics, osmotic pressures and tissue level flow.
Our paper on Inverse estimation of cardiac activation times via gradient-based optimisation is now published online in the International Journal for Numerical Methods in Biomedical Engineering! In this study, we use a PDE-constrained optimal control approach to numerically investigate the identifiability of an initial activation sequence from synthetic observations of the extracellular potential using the bidomain approximation and 2D representations of heart tissue. Our results demonstrate that activation times and duration of several stimuli can be recovered even with high levels of noise, that it is sufficient to sample the observations at the ECG-relevant sampling frequency of 1 kHz, and that spatial resolutions that are coarser than the standard in electrophysiological simulations can be used.
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.
In connection with the Women in PDEs workshop at the Karlsruhe Institute for Technology April 27-28 2017, Gudrun Thäter recorded a podcast conversation with me on the topic of cerebral fluid flow in general and the #Waterscales project in particular.
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: