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[CT117]

CT117 (1/1) : Numerical methods for partial differential equations, boundary value problems (65N) / Dynamics of a system of particles, including celestial mechanics (70F)

Session Time & Room : 5D (Aug.25, 15:30-17:10) @E705
Type : Contributed Talk
Abstract : In this talk, we present a systematic discretization of the Bernstein-Gelfand-Gelfand diagrams and complexes over cubical meshes of arbitrary dimension via the use of tensor-product structures of one-dimensional piecewise-polynomial spaces, such as spline and finite element spaces. We demonstrate the construction of the Hessian, the elasticity, and div-div complexes as examples for our construction.
Classification : 65N99, 41A15, 41A63, 65N30
Format : Talk at Waseda University
Author(s) :
- Duygu Sap (University of Oxford)
- Kaibo Hu (University of Oxford)
- Guido Kanschat (Heidelberg University)
- Francesca Bonizzoni (Politecnico di Milano)

Session Time & Room : 5D (Aug.25, 15:30-17:10) @E705
Type : Contributed Talk
Abstract : Sustained strong scalability is hard to sustain beyond 10K processors due to the communication and synchronisation involved in domain decomposition for PDEs. Seeking to overcome them, Spigler and Acebrón introduced probabilistic domain decomposition, which inserts stochastic calculus in the formulation---however with slow error convergence. I will present a hybrid idea, SpAc, which retains most of the scope for embarrassing parallelism, while being orders of magnitude faster. Proof of concept supercomputing simulations will be discussed.
Classification : 65Nxx
Format : Talk at Waseda University
Author(s) :
- Francisco Bernal (Carlos III University of Madrid)

Session Time & Room : 5D (Aug.25, 15:30-17:10) @E705
Type : Contributed Talk
Abstract : We present a priori and a posteriori error analysis to approximate the eigenvalues and eigenfunctions of the Stokes spectral problem. For the a priori analysis, we take advantage of the compactness of the solution operator to prove convergence of the eigenfunctions and eigenvalues. Additionally we propose a reliable and efficient a posteriori estimator in order to perform adaptive refinements that allow to recover the optimal order of convergence for non smooth eigenfunctions. We report some numerical tests
Classification : 65Nxx
Format : Talk at Waseda University
Author(s) :
- Felipe Lepe (Universidad del Bío Bío)

Session Time & Room : 5D (Aug.25, 15:30-17:10) @E705
Type : Contributed Talk
Abstract : Optical coherence elastography (OCE) is an imaging modality that maps mechanical properties by using optical coherence tomography (OCT) to measure tissue displacement after mechanical excitation. From OCE elastograms, quantified elasticity mapping can be accomplished using an appropriate mathematical model of the tissue. In this talk we present a mathematical model to reconstruct the mechanical properties of an elastic medium, in the OCE imaging technique. We formulate the inverse model problem as a PDE-constrained optimization problem, where the objective function measures the discrepancy between observations and predictions. We will discuss different strategies for learning the space varying elasticity coefficients.
Classification : 65Nxx, 65N21
Format : Talk at Waseda University
Author(s) :
- Silvia Barbeiro (University of Coimbra)
- Rafael Henriques (University of Coimbra)

Session Time & Room : 5D (Aug.25, 15:30-17:10) @E705
Type : Contributed Talk
Abstract : We consider the following inference problem for a system of interacting particles or agents: given only observed trajectories of the agents in the system, can we learn what the laws of interactions are? We would like to do this without assuming any particular form for the interaction laws, i.e. they might be “any” function of pairwise distances, or other variables. We discuss when this problem is well-posed, construct estimators for the interaction kernels with provably good statistically and computational properties, and discuss extensions to second-order systems, more general interaction kernels, and stochastic systems. We measure empirically the performance of our techniques on various examples, including families of systems with parametric interaction kernels, and settings where the interaction kernels depend on unknown variables. We also conduct numerical experiments to study the emergent behavior of these systems. This is joint work with F. Lu, J. Feng, P. Martin, J.Miller, S. Tang and M. Zhong.
Classification : 70F17, 62M20, 34A55
Format : Talk at Waseda University
Author(s) :
- Mauro Maggioni (Johns Hopkins University)