Biomedical Engineering Reference
In-Depth Information
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SUNDIALS (computation.llnl.gov/casc/sundials/main.html) for differential-alge-
braic equations;
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Hypre (computation.llnl.gov/casc/hypre/software.html) for preconditioners;
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TAO (mcs.anl.gov/research/projects/tao) for optimisation;
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SLEPc (grycap.upv.es/slepc) for eigenproblems;
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BLACS (netlib.org/blacs) and ScaLAPACK (netlib.org/scalapack) for linear al-
gebra.
For input and output OpenCMISS uses the CellML (cellml.org) and FieldML
(fieldml.org) APIs (Miller et al., 2010). FieldML will ultimately use standard libra-
ries such HDF5 (hdfgroup.org/HDF5) and/or NetCDF (unidata.ucar.edu/software/
netcdf) for parallel I/O of large data sets.
Multi-physics modelling
The major features in OpenCMISS for dealing with coupled multi-physics mod-
els include a flexible system for describing multiple physical models and complex
problem work flows, methods for coupling different physical systems together and
the ability to handle different spatial and temporal scales via FieldML concepts and
CellML models. In order to provide as general a modelling environment as possi-
ble OpenCMISS separates the equations and data that describe the physics from the
numerical and computational operations on those equations that make up the work-
flow for the problem. As the computational operations are then independent of the
physics, coupling different physical systems is easier as the overall solution process
can be formed by doing a sequence of numerical operations on a common system of
equations.
There are methods for coupling different physical systems of equations both in
the same region of interest and across different regions of interest. Coupled physics
in the same region uses a consistent FieldML description of each individual physical
problem and allows for coupled equations through the sharing of common variables.
Since each problem's associated data is stored using the same data structures, the in-
dividual equations for each problem can be formulated using variables from different
problems as easily as they can be formulated using variables from their problem.
Coupling across regions can be strong or weak. For strong coupling, different
equation sets from different physical systems are coupled together by allowing the
degrees-of-freedom (DOFs) in one set of equations to be linearly related to the DOFs
in another set of equations. This then allows for a strongly coupled set of equations
that govern the combined physics to be formed through row and column manipu-
lations of the individual equation sets. As inter-region coupling involves different
regions, the strong coupling is defined by using explicit interfaces. These interfaces
ensure that information is passed between regions in a controlled manner.
For weak coupling an intermediate object is used to relate the equation data in
one region with the equation data in a neighbouring region. The intermediate ob-
ject can then store the information that is required to couple the DOFs in a weak, or
integral, sense. Examples of weak methods supported by OpenCMISS include La-
grange, augmented Lagrange and penalty methods. For the weak coupling methods
