arXiv subjects

Erik Henningsson

Publications and source records attributed to Erik Henningsson.

5 recordsLinked to original sources

arXiv2026

Towards an FMI Layered Standard for DAE: Applications for Simulation and Optimization

The Functional Mock-up Interface (FMI) 3.0 standard for Model Exchange is restricted to hybrid ordinary differential equations, requiring any internal algebraic equations to be solved inside the Functional Mock-up Unit (FMU) before derivatives are returned to the importer. For models originating from, e.g. Modelica, this means that non-linear algebraic equations must be solved through internal Newton iterations, which can reduce accuracy, increase computational cost, introduce hidden solver states, and cause robustness issues in downstream simulation and optimization workflows. In this article, we present a proposal for a layered standard, fmi-ls-dae, that exposes algebraic equations and their associated algebraic variables as part of a semi-explicit index-1 differential-algebraic equation. We describe the proposed extensions to the FMI XML schema and demonstrate the approach through prototype implementations: Dymola and CasADi generate FMUs that expose this semi-explicit index-1 formulation, while CasADi, FMIOPT, Simcenter Twin Activate, fmusim, and MOO (the dynamic optimization tool of OpenModelica) import them for simulation and dynamic optimization. On an industrially relevant multilink suspension corner model, the proposed DAE-FMU formulation enables the optimization routine to converge on an optimal control problem on which the equivalent ODE-FMU fails to converge. We outline ongoing work towards consistent initialization, event handling and future support for higher-index DAEs.

eess.SY↗

arXiv2018

Additive domain decomposition operator splittings -- convergence analyses in a dissipative framework

We analyze temporal approximation schemes based on overlapping domain decompositions. As such schemes enable computations on parallel and distributed hardware, they are commonly used when integrating large-scale parabolic systems. Our analysis is conducted by first casting the domain decomposition procedure into a variational framework based on weighted Sobolev spaces. The time integration of a parabolic system can then be interpreted as an operator splitting scheme applied to an abstract evolution equation governed by a maximal dissipative vector field. By utilizing this abstract setting, we derive an optimal temporal error analysis for the two most common choices of domain decomposition based integrators. Namely, alternating direction implicit schemes and additive splitting schemes of first and second order. For the standard first-order additive splitting scheme we also extend the error analysis to semilinear evolution equations, which may only have mild solutions.

math.NA↗

arXiv2016

Efficient simulations of tubulin-driven axonal growth

This work concerns efficient and reliable numerical simulations of the dynamic behaviour of a moving-boundary model for tubulin-driven axonal growth. The model is nonlinear and consists of a coupled set of a partial differential equation (PDE) and two ordinary differential equations. The PDE is defined on a computational domain with a moving boundary, which is part of the solution. Numerical simulations based on standard explicit time-stepping methods are too time consuming due to the small time steps required for numerical stability. On the other hand standard implicit schemes are too complex due to the nonlinear equations that needs to be solved in each step. Instead, we propose to use the Peaceman--Rachford splitting scheme combined with temporal and spatial scalings of the model. Simulations based on this scheme have shown to be efficient, accurate, and reliable which makes it possible to evaluate the model, e.g.\ its dependency on biological and physical model parameters. These evaluations show among other things that the initial axon growth is very fast, that the active transport is the dominant reason over diffusion for the growth velocity, and that the polymerization rate in the growth cone does not affect the final axon length.

q-bio.CB↗

arXiv2015

A Convergence Analysis of the Peaceman--Rachford Scheme for Semilinear Evolution Equations

The Peaceman--Rachford scheme is a commonly used splitting method for discretizing semilinear evolution equations, where the vector fields are given by the sum of one linear and one nonlinear dissipative operator. Typical examples of such equations are reaction-diffusion systems and the damped wave equation. In this paper we conduct a convergence analysis for the Peaceman--Rachford scheme in the setting of dissipative evolution equations on Hilbert spaces. We do not assume Lipschitz continuity of the nonlinearity, as previously done in the literature. First or second order convergence is derived, depending on the regularity of the solution, and a shortened proof for $o(1)$-convergence is given when only a mild solution exits. The analysis is also extended to the Lie scheme in a Banach space framework. The convergence results are illustrated by numerical experiments for Caginalp's solidification model and the Gray--Scott pattern formation problem.

math.NA↗

arXiv2015

A full space-time convergence order analysis of operator splittings for linear dissipative evolution equations

The Douglas--Rachford and Peaceman--Rachford splitting methods are common choices for temporal discretizations of evolution equations. In this paper we combine these methods with spatial discretizations fulfilling some easily verifiable criteria. In the setting of linear dissipative evolution equations we prove optimal convergence orders, simultaneously in time and space. We apply our abstract results to dimension splitting of a 2D diffusion problem, where a finite element method is used for spatial discretization. To conclude, the convergence results are illustrated with numerical experiments.

math.NA↗