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

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

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

Route Planning in Transportation Networks

We survey recent advances in algorithms for route planning in transportation networks. For road networks, we show that one can compute driving directions in milliseconds or less even at continental scale. A variety of techniques provide different trade-offs between preprocessing effort, space requirements, and query time. Some algorithms can answer queries in a fraction of a microsecond, while others can deal efficiently with real-time traffic. Journey planning on public transportation systems, although conceptually similar, is a significantly harder problem due to its inherent time-dependent and multicriteria nature. Although exact algorithms are fast enough for interactive queries on metropolitan transit systems, dealing with continent-sized instances requires simplifications or heavy preprocessing. The multimodal route planning problem, which seeks journeys combining schedule-based transportation (buses, trains) with unrestricted modes (walking, driving), is even harder, relying on approximate solutions even for metropolitan inputs.Comment: This is an updated version of the technical report MSR-TR-2014-4, previously published by Microsoft Research. This work was mostly done while the authors Daniel Delling, Andrew Goldberg, and Renato F. Werneck were at Microsoft Research Silicon Valle

Distributed-memory large deformation diffeomorphic 3D image registration

We present a parallel distributed-memory algorithm for large deformation diffeomorphic registration of volumetric images that produces large isochoric deformations (locally volume preserving). Image registration is a key technology in medical image analysis. Our algorithm uses a partial differential equation constrained optimal control formulation. Finding the optimal deformation map requires the solution of a highly nonlinear problem that involves pseudo-differential operators, biharmonic operators, and pure advection operators both forward and back- ward in time. A key issue is the time to solution, which poses the demand for efficient optimization methods as well as an effective utilization of high performance computing resources. To address this problem we use a preconditioned, inexact, Gauss-Newton- Krylov solver. Our algorithm integrates several components: a spectral discretization in space, a semi-Lagrangian formulation in time, analytic adjoints, different regularization functionals (including volume-preserving ones), a spectral preconditioner, a highly optimized distributed Fast Fourier Transform, and a cubic interpolation scheme for the semi-Lagrangian time-stepping. We demonstrate the scalability of our algorithm on images with resolution of up to $1024^3$ on the "Maverick" and "Stampede" systems at the Texas Advanced Computing Center (TACC). The critical problem in the medical imaging application domain is strong scaling, that is, solving registration problems of a moderate size of $256^3$---a typical resolution for medical images. We are able to solve the registration problem for images of this size in less than five seconds on 64 x86 nodes of TACC's "Maverick" system.Comment: accepted for publication at SC16 in Salt Lake City, Utah, USA; November 201