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We introduce an a posteriori modeling error estimator for the effective computation of electric potential propagation in the heart. Starting from the Bidomain problem and an extended formulation of the simplified Monodomain system, we build a hybrid model, called Hybridomain, which is dynamically adapted to be either Bi- or Monodomain ones in different regions of the computational domain according to the error estimator. We show that accurate results can be obtained with the adaptive Hybridomain model with a reduced computational cost compared to the full Bidomain model. We discuss the effectivity of the estimator and the reliability of the results on simulations performed on real human left ventricle geometries retrieved from healthy subjects.

We are interested in the simulation and optimization of gas transport in networks. Those networks consist of pipes and various other components like compressor stations and valves. The gas flow through the pipes can be modelled by different equations based on the Euler equations. For the other components, purely algebraic equations are used. Depending on the data, different models for the gas flow can be used in different regions of the network. We use adjoint techniques to specify model and discretization error estimators and present a strategy that adaptively applies the different models while maintaining the accuracy of the solution.

We introduce an a posteriori modeling error estimator for the effective computation of electric potential propagation in the heart. Starting from the Bidomain problem and an extended formulation of the simplified Monodomain system, we build a hybrid model, called Hybridomain, which is dynamically adapted to be either Bi- or Monodomain ones in different regions of the computational domain according to the error estimator. We show that accurate results can be obtained with the adaptive Hybridomain model with a reduced computational cost compared to the full Bidornain model. We discuss the effectivity of the estimator and the reliability of the results on simulations performed on real human left ventricle geometries retrieved from healthy subjects. (C) 2010 Elsevier B.V. All rights reserved.