Sparse spectral-tau method for the three-dimensional helically reduced wave equation on two-center domains

We describe a multidomain spectral-tau method for solving the three-dimensional helically reduced wave equation on the type of two-center domain that arises when modeling compact binary objects in astrophysical applications. A global two-center domain may arise as the union of Cartesian blocks, cylindrical shells, and inner and outer spherical shells. For each such subdomain, our key objective is to realize certain (differential and multiplication) physical-space operators as matrices acting on the corresponding set of modal coefficients. We achieve sparse banded realizations through the integration "preconditioning" of Coutsias, Hagstrom, Hesthaven, and Torres. Since ours is the first three-dimensional multidomain implementation of the technique, we focus on the issue of convergence for the global solver, here the alternating Schwarz method accelerated by GMRES. Our methods may prove relevant for numerical solution of other mixed-type or elliptic problems, and in particular for the generation of initial data in general relativity.Comment: 37 pages, 3 figures, 12 table

Self-adapting structuring and representation of space

The objective of this report is to propose a syntactic formalism for space representation. Beside the well known advantages of hierarchical data structure, the underlying approach has the additional strength of self-adapting to a spatial structure at hand. The formalism is called puzzletree because its generation results in a number of blocks which in a certain order -- like a puzzle - reconstruct the original space. The strength of the approach does not lie only in providing a compact representation of space (e.g. high compression), but also in attaining an ideal basis for further knowledge-based modeling and recognition of objects. The approach may be applied to any higher-dimensioned space (e.g. images, volumes). The report concentrates on the principles of puzzletrees by explaining the underlying heuristic for their generation with respect to 2D spaces, i.e. images, but also schemes their application to volume data. Furthermore, the paper outlines the use of puzzletrees to facilitate higher-level operations like image segmentation or object recognition. Finally, results are shown and a comparison to conventional region quadtrees is done

Extending a serial 3D two-phase CFD code to parallel execution over MPI by using the PETSc library for domain decomposition

To leverage the last two decades' transition in High-Performance Computing (HPC) towards clusters of compute nodes bound together with fast interconnects, a modern scalable CFD code must be able to efficiently distribute work amongst several nodes using the Message Passing Interface (MPI). MPI can enable very large simulations running on very large clusters, but it is necessary that the bulk of the CFD code be written with MPI in mind, an obstacle to parallelizing an existing serial code. In this work we present the results of extending an existing two-phase 3D Navier-Stokes solver, which was completely serial, to a parallel execution model using MPI. The 3D Navier-Stokes equations for two immiscible incompressible fluids are solved by the continuum surface force method, while the location of the interface is determined by the level-set method. We employ the Portable Extensible Toolkit for Scientific Computing (PETSc) for domain decomposition (DD) in a framework where only a fraction of the code needs to be altered. We study the strong and weak scaling of the resulting code. Cases are studied that are relevant to the fundamental understanding of oil/water separation in electrocoalescers.Comment: 8 pages, 6 figures, final version for to the CFD 2014 conferenc

Surveillance centric coding

PhDThe research work presented in this thesis focuses on the development of techniques specific to surveillance videos for efficient video compression with higher processing speed. The Scalable Video Coding (SVC) techniques are explored to achieve higher compression efficiency. The framework of SVC is modified to support Surveillance Centric Coding (SCC). Motion estimation techniques specific to surveillance videos are proposed in order to speed up the compression process of the SCC. The main contributions of the research work presented in this thesis are divided into two groups (i) Efficient Compression and (ii) Efficient Motion Estimation. The paradigm of Surveillance Centric Coding (SCC) is introduced, in which coding aims to achieve bit-rate optimisation and adaptation of surveillance videos for storing and transmission purposes. In the proposed approach the SCC encoder communicates with the Video Content Analysis (VCA) module that detects events of interest in video captured by the CCTV. Bit-rate optimisation and adaptation are achieved by exploiting the scalability properties of the employed codec. Time segments containing events relevant to surveillance application are encoded using high spatiotemporal resolution and quality while the irrelevant portions from the surveillance standpoint are encoded at low spatio-temporal resolution and / or quality. Thanks to the scalability of the resulting compressed bit-stream, additional bit-rate adaptation is possible; for instance for the transmission purposes. Experimental evaluation showed that significant reduction in bit-rate can be achieved by the proposed approach without loss of information relevant to surveillance applications. In addition to more optimal compression strategy, novel approaches to performing efficient motion estimation specific to surveillance videos are proposed and implemented with experimental results. A real-time background subtractor is used to detect the presence of any motion activity in the sequence. Different approaches for selective motion estimation, GOP based, Frame based and Block based, are implemented. In the former, motion estimation is performed for the whole group of pictures (GOP) only when a moving object is detected for any frame of the GOP. iii While for the Frame based approach; each frame is tested for the motion activity and consequently for selective motion estimation. The selective motion estimation approach is further explored at a lower level as Block based selective motion estimation. Experimental evaluation showed that significant reduction in computational complexity can be achieved by applying the proposed strategy. In addition to selective motion estimation, a tracker based motion estimation and fast full search using multiple reference frames has been proposed for the surveillance videos. Extensive testing on different surveillance videos shows benefits of application of proposed approaches to achieve the goals of the SCC

Compact binary evolutions with the Z4c formulation

Numerical relativity simulations of compact binaries with the Z4c and BSSNOK formulations are compared. The Z4c formulation is advantageous in every case considered. In simulations of non-vacuum spacetimes the constraint violations due to truncation errors are between one and three orders of magnitude lower in the Z4c evolutions. Improvements are also found in the accuracy of the computed gravitational radiation. For equal-mass irrotational binary neutron star evolutions we find that the absolute errors in phase and amplitude of the waveforms can be up to a factor of four smaller. The quality of the Z4c numerical data is also demonstrated by a remarkably accurate computation of the ADM mass from surface integrals. For equal-mass non-spinning binary puncture black hole evolutions we find that the absolute errors in phase and amplitude of the waveforms can be up to a factor of two smaller. In the same evolutions we find that away from the punctures the Hamiltonian constraint violation is reduced by between one and two orders of magnitude. Furthermore, the utility of gravitational radiation controlling, constraint preserving boundary conditions for the Z4c formulation is demonstrated. The evolution of spacetimes containing a single compact object confirm earlier results in spherical symmetry. The boundary conditions avoid spurious and non-convergent effects present in high resolution runs with either formulation with a more naive boundary treatment. We conclude that Z4c is preferable to BSSNOK for the numerical solution of the 3+1 Einstein equations with the puncture gauge