CNSPACK
Compact Non-symmetric Solver PACKage
Software for iterative solution of large sparse linear algebraic systems with preconditioning by high order incomplete decomposition.
Computer simulations of physical phenomena
Scientific and engineering computer simulations of physical phenomena in application areas such as:
- Aerodynamics, Fluid flows, Shock waves, Missiles, Explosions
- Semiconductor devices, Electronic circuits
- Solar cells, Nanoelectronics, Optoelectronics
- Electromagnetics, RF-cavities, Waveguides
- Radiation effects in semiconductor devices
- Etc.
are based on solutions of the Partial Differential Equations (PDE), like Maxwell equations, Navier Stokes equation, Schrödinger equation, Boltzmann equation etc.
The approximate solution of such equation is based on finite-element method, finite volume method, finite difference method. These methods convert PDE into in a large sparse system of linear equations at each moment of time, where the unknowns are the physical values of pressure, density, temperature, electric field, electron concentration etc. at different locations in space at that fixed time.
To simulate the phenomenon changing with time, one need to solve these very large sparse systems of linear equations many times, say typically million times. Therefore the linear system solver becomes a critical element of such a software.
Comparison of performance of CNSPACK to best industry linear solvers:
CNSPACK solves a typical industrial problem faster by a factor 10 to 100, and need less computer memory by a factor of 10. A particular example presented in publication:
(a) CNSPACK when used in commercial 3D device simulator TCAD results in less computer memory by a factor of 10, and CPU time is smaller by several times for similar problems compared to competitors.
(b) Data from the University that used TCAD (with CNSPACK) and another famous TCAD for simulation of radiation effects in semiconductor devices caused by ionizing particles: simulation time about one month for others a day for CNSPACK.
(a) Comparison of the scalar CNSPACK performance versus other solvers (pink, lower curve) for coupled 3D CFD problem.
Theoretical asymptotic for direct and preconditioned iterative methods, the N (upper light blue line) and N^(5/4) (dotted blue) lines, are plotted for comparison.
(b) NanoTCAD simulator performance for modeling 3D devices: memory, solid curve with diamonds (in MB), and CPU time, solid curve with circles (in s/N iteration) versus number of mesh nodes. One can see that dependence is almost linear for both memory and CPU time and close to the theoretical estimate for the CPU time, T = 0(N^(5/4)) (dashed curve)