45,644 research outputs found

    High-order Finite Volume WENO schemes for non-local multi-class traffic flow models

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    International audienceThis paper focuses on the numerical approximation of a class of non-local systems of conservation laws in one space dimension, arising in traffic modeling, proposed by [F. A. Chiarello and P. Goatin. Non-local multi-class traffic flow models. Networks and Heterogeneous Media, to appear, Aug. 2018]. We present the multi-class version of the Finite Volume WENO (FV-WENO) schemes [C. Chalons, P. Goatin, and L. M. Villada. High-order numerical schemes for one-dimensional non-local conservation laws. SIAM Journal on Scientific Computing, 40(1):A288-A305, 2018.], with quadratic polynomial reconstruction in each cell to evaluate the non-local terms in order to obtain high-order of accuracy. Simulations using FV-WENO schemes for a multi-class model for autonomous and human-driven traffic flow are presented for M = 3

    High-order Finite Volume WENO schemes for non-local multi-class traffic flow models

    Get PDF
    International audienceThis paper focuses on the numerical approximation of a class of non-local systems of conservation laws in one space dimension, arising in traffic modeling, proposed by [F. A. Chiarello and P. Goatin. Non-local multi-class traffic flow models. Networks and Heterogeneous Media, to appear, Aug. 2018]. We present the multi-class version of the Finite Volume WENO (FV-WENO) schemes [C. Chalons, P. Goatin, and L. M. Villada. High-order numerical schemes for one-dimensional non-local conservation laws. SIAM Journal on Scientific Computing, 40(1):A288-A305, 2018.], with quadratic polynomial reconstruction in each cell to evaluate the non-local terms in order to obtain high-order of accuracy. Simulations using FV-WENO schemes for a multi-class model for autonomous and human-driven traffic flow are presented for M = 3

    Recycling BiCGSTAB with an Application to Parametric Model Order Reduction

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    Krylov subspace recycling is a process for accelerating the convergence of sequences of linear systems. Based on this technique, the recycling BiCG algorithm has been developed recently. Here, we now generalize and extend this recycling theory to BiCGSTAB. Recycling BiCG focuses on efficiently solving sequences of dual linear systems, while the focus here is on efficiently solving sequences of single linear systems (assuming non-symmetric matrices for both recycling BiCG and recycling BiCGSTAB). As compared with other methods for solving sequences of single linear systems with non-symmetric matrices (e.g., recycling variants of GMRES), BiCG based recycling algorithms, like recycling BiCGSTAB, have the advantage that they involve a short-term recurrence, and hence, do not suffer from storage issues and are also cheaper with respect to the orthogonalizations. We modify the BiCGSTAB algorithm to use a recycle space, which is built from left and right approximate invariant subspaces. Using our algorithm for a parametric model order reduction example gives good results. We show about 40% savings in the number of matrix-vector products and about 35% savings in runtime.Comment: 18 pages, 5 figures, Extended version of Max Planck Institute report (MPIMD/13-21
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