In article <1992May17.233022.9192 at news.arc.nasa.gov> doshay at ursa.arc.nasa.gov (David Doshay) writes:
>In my case this does not work because the 2d tissue that we also model
>is not tridiagonal at all, though it can be properly ordered to be strongly
>diagonally dominant. We could use the Hines method on all the branched
>cables, using other methods when we do the 2d tissue, but at this point
>we are using a sparce matrix solver that is relatively fast without adding
>the complication of using 2 different methods for different parts of the
>total matrix. We will probably add a preconditioner, that does what is
>essentially a generalization of the Hines technique, when our data sets
>get larger. At this point we have not yet seen that it will speed us up
>enough to implement it.
You might look into relaxation techniques for solving the matrix -
these require diagonally-dominant matrices which in general is the
case for syncytium or neurons because of the membrane capacitance.
These techniques have been applied to VLSI simulations:
@InProceedings(Webb-87,
Author = {Webber, D. and Sangiovanni-Vincentelli, A.},
Title = {Circuit Simulation on the Connection Machine},
BookTitle = {Design Automation Conf.},
Year = {1987}
)
@Book(Whit-86,
Author = {White, J. and Sangiovanni-Vincentelli, A.},
Title = {Relaxation Techniques for the Simulation of VLSI Circuits},
Publisher = {Kluwer},
Year = {1986}
)
Lyle
