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- Jjrgen Sand, 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 subsystems. The formulas are called decoupled backward differentiation formulas, and they are derived from the classical formulas by restricting the implicit part to the diagonal subsystem.… (More)

In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier's archiving and manuscript policies are encouraged to visit: Keywords: Quantum transport Density functional theory Green's function Cyclic… (More)

Large air pollution models are commonly used to study trans-boundary 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)

Dynamical systems can often be decomposed into loosely coupled subsystems. The system of ordinary diierential 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)

- Stig Skelboe
- 2006

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
- 2010

Many implicit differential equations (IDEs) modelling 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 compared to solving… (More)

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)

- Stig Skelboe
- PARA
- 1996

Partitioned systems of ordinary differential equations are in qualitative terms characterized as monotonically max-norm stable if each subsystem is stable and if the couplings from one subsystem to the others are weak. Each subsystem of the partitioned system may be discretized independently by the backward Euler formula using solution values from the other… (More)