Deposits of clastic carbonate-dominated (calciclastic) sedimentary slope systems in the rock record have been identified mostly as linearly-consistent carbonate apron deposits, even though most ancient clastic carbonate slope deposits fit the submarine fan systems better. Calciclastic submarine fans are consequently rarely described and are poorly understood. Subsequently, very little is known especially in mud-dominated calciclastic submarine fan systems. Presented in this study are a sedimentological core and petrographic characterisation of samples from eleven boreholes from the Lower Carboniferous of Bowland Basin (Northwest England) that reveals a >250 m thick calciturbidite complex deposited in a calciclastic submarine fan setting. Seven facies are recognised from core and thin section characterisation and are grouped into three carbonate turbidite sequences. They include: 1) Calciturbidites, comprising mostly of highto low-density, wavy-laminated bioclast-rich facies; 2) low-density densite mudstones which are characterised by planar laminated and unlaminated muddominated facies; and 3) Calcidebrites which are muddy or hyper-concentrated debrisflow deposits occurring as poorly-sorted, chaotic, mud-supported floatstones. These

Phd by thesis

We describe the University of Florida Sparse Matrix Collection, a large and actively growing set of sparse matrices that arise in real applications The Collection is widely used by the numerical linear algebra community for the development and performance evaluation of sparse matrix algorithms It allows for robust and repeatable experiments: robust because performance results with artificially generated matrices can be misleading, and repeatable because matrices are curated and made publicly available in many formats Its matrices cover a wide spectrum of domains, include those arising from problems with underlying 2D or 3D geometry (as structural engineering, computational fluid dynamics, model reduction, electromagnetics, semiconductor devices, thermodynamics, materials, acoustics, computer graphics/vision, robotics/kinematics, and other discretizations) and those that typically do not have such geometry (optimization, circuit simulation, economic and financial modeling, theoretical and quantum chemistry, chemical process simulation, mathematics and statistics, power networks, and other networks and graphs) We provide software for accessing and managing the Collection, from MATLAB™, Mathematica™, Fortran, and C, as well as an online search capability Graph visualization of the matrices is provided, and a new multilevel coarsening scheme is proposed to facilitate this task

The university of Florida sparse matrix collection

This is a short presentation of the freefem++ software. In Section 1, we recall most of the characteristics of the software, In Section 2, we recall how to to build the weak form of a partial differential equation (PDE) from the strong form. In the 3 last sections, we present different examples and tools to illustrated the power of the software. First we deal with mesh adaptation for problems in two and three dimension, second, we solve numerically a problem with phase change and natural convection, and the finally to show the possibilities for HPC we solve a Laplace equation by a Schwarz domain decomposition problem on parallel computer.

/pdf/new-development-in-freefem-1kqm5xe63f.pdf

New development in freefem

Large linear systems of saddle point type arise in a wide variety of applications throughout computational science and engineering. Due to their indefiniteness and often poor spectral properties, such linear systems represent a significant challenge for solver developers. In recent years there has been a surge of interest in saddle point problems, and numerous solution techniques have been proposed for this type of system. The aim of this paper is to present and discuss a large selection of solution methods for linear systems in saddle point form, with an emphasis on iterative methods for large and sparse problems.

/pdf/numerical-solution-of-saddle-point-problems-l583iob5c2.pdf

Numerical solution of saddle point problems

We consider the problem of designing a dynamic scheduling strategy that takes into account both workload and memory information in the context of the parallel multifrontal factorization. The originality of our approach is that we base our estimations (work and memory) on a static optimistic scenario during the analysis phase. This scenario is then used during the factorization phase to constrain the dynamic decisions that compute fully irregular partitions in order to better balance the workload. We show that our new scheduling algorithm significantly improves both the memory behaviour and the factorization time. We give experimental results for large challenging real-life 3D problems on 64 and 128 processors.

/pdf/hybrid-scheduling-for-the-parallel-solution-of-linear-7h62u6cen9.pdf

Hybrid scheduling for the parallel solution of linear systems

We consider ways of implementing preordering and scaling for symmetric systems and show the effect of using this technique with a multifrontal code for sparse symmetric indefinite systems. After having presented a new method for scaling, we propose a way of using an approximation to a symmetric weighted matching to predefine $1 \times 1$ and $2 \times 2$ pivots prior to the ordering and analysis phase. We also present new classes of orderings called "(relaxed) constrained orderings" that mix structural and numerical criteria.

/pdf/strategies-for-scaling-and-pivoting-for-sparse-symmetric-1sxi9jx94s.pdf

Strategies for Scaling and Pivoting for Sparse Symmetric Indefinite Problems

We consider the direct solution of sparse symmetric indefinite matrices. We develop new pivoting strategies that combine numerical pivoting and perturbation techniques. Then an iterative refinement process uses our approximate factorization to compute a solution. We show that our pivoting strategies are numerically robust, that few steps of iterative refinement are required, and that the factorization is significantly faster than with previous methods. Furthermore, we propose original approaches that are designed for parallel distributed factorization. A key point of our parallel implementation is the cheap and reliable estimation of the growth factor. This estimation is based on an approximation of the off-diagonal entries and does not require any supplementary messages.

Towards Stable Mixed Pivoting Strategies for the Sequential and Parallel Solution of Sparse Symmetric Indefinite Systems

A strict adherence to threshold pivoting in the direct solution of symmetric indefinite problems can result in substantially more work and storage than forecast by a sparse analysis of the symmetric problem. One way of avoiding this is to use static pivoting where the data structures and pivoting sequence generated by the analysis are respected and pivots that would otherwise be very small are replaced by a user defined quantity. This can give a stable factorization but of a perturbed matrix. The conventional way of solving the sparse linear system is then to use iterative refinement, but there are cases where this fails to converge. In this paper, we discuss the use of more robust iterative methods, namely GMRES and flexible GMRES (FGMRES). We show both theoretically and experimentally that both approaches are more robust than iterative refinement and furthermore that FGMRES is far more robust than GMRES and that, under reasonable hypotheses, FGMRES is backward stable. We also show how restarted variants can be beneficial, although again the GMRES variant is not as robust as FGMRES.

/pdf/a-note-on-gmres-preconditioned-by-a-perturbed-l-d-l-t-4p3zw9smg5.pdf

A Note on GMRES Preconditioned by a Perturbed $L D L^T$ Decomposition with Static Pivoting

We consider the direct solution of general sparse linear systems baseds on a multifrontal method. The approach combines partial static scheduling of the task dependency graph during the symbolic factorization and distributed dynamic scheduling during the numerical factorization to balance the work among the processes of a distributed memory computer. We show that to address clusters of Symmetric Multi-Processor (SMP) architectures, and more generally non-uniform memory access multiprocessors, our algorithms for both the static and the dynamic scheduling need to be revisited to take account of the non-uniform cost of communication. The performance analysis on an IBM SP3 with 16 processors per SMP node and up to 128 processors shows that we can significantly reduce both the amount of inter-node communication and the solution time.

Stéphane Pralet

Papers

Hybrid scheduling for the parallel solution of linear systems

Strategies for Scaling and Pivoting for Sparse Symmetric Indefinite Problems

Towards Stable Mixed Pivoting Strategies for the Sequential and Parallel Solution of Sparse Symmetric Indefinite Systems

A Note on GMRES Preconditioned by a Perturbed $L D L^T$ Decomposition with Static Pivoting

Adapting a parallel sparse direct solver to architectures with clusters of SMPs