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- Stig Skelboe
- 1992

For a large class of traditional backward Euler multirate methods we show that stability is preserved when the methods are applied to certain stable (but not necessarily monotonic) non-linear systems. Methods which utilize waveform relaxation sweeps are shown to be stable and converge for certain monotonic systems. 1 Relaxing the monotonicity condition… (More)

- Stig Skelboe
- 1992

This paper presents a class of parallel numerical integration methods for stiff systems of ordinary differential equations which can be partitioned into loosely coupled sub-systems. The formulas are called decoupled backward differentiation formulas, and they are derived from the classical formulas by restricting the implicit part to the diagonal… (More)

- Stig Skelboe
- SIAM J. Scientific Computing
- 2000

Dynamical systems can often be decomposed into loosely coupled subsystems. The system of ordinary differential equations (ODEs) modelling such a problem can then be partitioned corresponding to the subsystems, and the loose couplings can be exploited by special integration methods to solve the problem using a parallel computer or just solve the problem more… (More)

- Dan Erik Petersen, Song Li, +4 authors Eric Darve
- J. Comput. Physics
- 2009

Quantum transport models for nanodevices using the non-equilibrium Green’s function method require the repeated calculation of the block tridiagonal part of the Green’s and lesser Green’s function matrices. This problem is related to the calculation of the inverse of a sparse matrix. Because of the large number of times this calculation needs to be… (More)

- Stig Skelboe, Zahari Zlatev
- WNAA
- 1996

Large air pollution models are commonly used to study transboundary transport of air pollutants. Such models are described mathematically by systems of partial differential equations (the number of equations being equal to the number of pollutants involved in the model). The use of appropriate splitting procedures leads to several sub-models. If the model… (More)

- Ibrahim N. Hajj, Stig Skelboe
- Parallel Computing
- 1990

- Dan Erik Petersen, Hans Henrik B. Sørensen, Per Christian Hansen, Stig Skelboe, Kurt Stokbro
- J. Comput. Physics
- 2008

A method for the inversion of block tridiagonal matrices encountered in electronic structure calculations is developed, with the goal of efficiently determining the matrices involved in the Fisher–Lee relation for the calculation of electron transmission coefficients. The new method leads to faster transmission calculations compared to traditional methods,… (More)

Many stiff systems of ordinary differential equations (ODEs) modeling practical problems can be partitioned into loosely coupled subsystems. In this paper the objective of the partitioning is to permit the numerical integration of one time step to be performed as the solution of a sequence of small subproblems. This reduces the computational complexity… (More)

- Stig Skelboe
- 1991

The DC analysis and transient analysis parts of the general electrical circuit analysis program ESACAP are parallelized to run on the Intel iPSC. Most of the program runs unchanged on the cube manager. Only the solution of the systems of nonlinear algebraic equations is parallelized to run on the hypercube parallel computer. The nonlinear equations arise… (More)