Analysis and implementation of anefficient solver for large-scalesimulations of neuronal systems

Sammanfattning: Numerical integration methods exploiting the characteristics of neuronal equation systems were investigated. The main observations was a high stiffness and a quasi-linearity of the system. The latter allowed for decomposition into two smaller systems by using a block diagonal Jacobian approximation. The popular backwards differentiation formulas methods (BDF) showed performance degradation for this during first experiments. Linearly implicit peer methods (PeerLI), a new class of methods, did not show this degradation. Parameters for PeerLI were optimized by experimental means and then compared in performance to BDF. Models were simulated in both Matlab and NEURON, a neuron modelling package. For small models PeerLI was competitive with BDF, especially with a block diagonal Jacobian. In NEURON the performance of the block diagonal Jacobian did no longer degrade for BDF, but instead showed degradation for PeerLI, especially for large models. With full Jacobian PeerLI was competitive with BDF, but with block diagonal Jacobian an increase of ca.50% was seen in simulation time. Overall PeerLI methods were competitive for certain problems, but did not give the desired performance gain for block diagonal Jacobian for large problems. There is, however, still a lot of room for improvement, since parameters were only determined experimentally and tuned to small problems.