@misc{Heroth, author = {Heroth, J{\"o}rg}, title = {Are Sparse Grids Suitable for the Tabulation of Reduced Chemical Systems?}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-5441}, number = {TR-97-02}, abstract = {Reduced chemical systems are used in the numerical simulation of combustion processes. An automatic approach to generate a reduced model is the so-called intrinsic-low-dimensional manifold (ILDM) by {\sc Maas and Pope}. Thereby, the system state is tabulated as a function of some parameters. The paper analyses the storage requirements for usual interpolation schemes and for sparse grids. It also estimates the response time and gives a short description of an implementation.}, language = {en} } @misc{DeuflhardHerothMaas, author = {Deuflhard, Peter and Heroth, J{\"o}rg and Maas, Ulrich}, title = {Towards Dynamical Dimension Reduction in Reactive Flow Problems}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-2383}, number = {SC-96-27}, abstract = {The paper addresses the possibilities of reducing the overall number of degrees of freedom in large scale reactive flow computations. Attention focusses on the dimension reduction technique ILDM due to {\sc Maas and Pope}, which treats certain automatically detected fast dynamic components as algebraic equations (so-called slow manifold). In earlier papers, the dimension of the reduction had been kept constant throughout each computation. Recently, a mathematically sound and nevertheless cheap dimension monitor for the chemistry part only has been suggested by {\sc Deuflhard and Heroth}. The present paper reports about first steps taken towards the implementation of that monitor into a flame code. Moreover, a sparse grid storage scheme is advocated and analyzed in view of the construction of efficient table look--ups for nested manifolds.}, language = {en} } @misc{DeuflhardHeroth, author = {Deuflhard, Peter and Heroth, J{\"o}rg}, title = {Dynamic Dimension Reduction in ODE Models}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-1951}, number = {SC-95-29}, abstract = {The paper analyzes a splitting technique into fast and slow dynamical components of ODE systems as suggested by {\sc Maas and Pope} recently. Their technique is based on a real block -- Schur decomposition of the Jacobian of the right hand side of the ODE. As a result of the analysis, a computationally cheap monitor for the possible necessary recovering of the splitting is derived by singular perturbation theory. Numerical experiments on moderate size, but challenging reaction kinetics problems document the efficiency of the new device within a linearly-implicit stiff integrator.}, language = {en} }