A domain decomposition strategy to efficiently solve structures containing repeated patterns

This paper presents a strategy for the computation of structures with repeated patterns based on domain decomposition and block Krylov solvers. It can be seen as a special variant of the FETI method. We propose using the presence of repeated domains in the problem to compute the solution by minimizing the interface error on several directions simultaneously. The method not only drastically decreases the size of the problems to solve but also accelerates the convergence of interface problem for nearly no additional computational cost and minimizes expensive memory accesses. The numerical performances are illustrated on some thermal and elastic academic problems

A Combinatorial Problem Related to Sparse Systems of Equations

Nowadays sparse systems of equations occur frequently in science and engineering. In this contribution we deal with sparse systems common in cryptanalysis. Given a cipher system, one converts it into a system of sparse equations, and then the system is solved to retrieve either a key or a plaintext. Raddum and Semaev proposed new methods for solving such sparse systems. It turns out that a combinatorial MaxMinMax problem provides bounds on the average computational complexity of sparse systems. In this paper we initiate a study of a linear algebra variation of this MaxMinMax problem

GPU Accelerated Explicit Time Integration Methods for Electro-Quasistatic Fields

Electro-quasistatic field problems involving nonlinear materials are commonly discretized in space using finite elements. In this paper, it is proposed to solve the resulting system of ordinary differential equations by an explicit Runge-Kutta-Chebyshev time-integration scheme. This mitigates the need for Newton-Raphson iterations, as they are necessary within fully implicit time integration schemes. However, the electro-quasistatic system of ordinary differential equations has a Laplace-type mass matrix such that parts of the explicit time-integration scheme remain implicit. An iterative solver with constant preconditioner is shown to efficiently solve the resulting multiple right-hand side problem. This approach allows an efficient parallel implementation on a system featuring multiple graphic processing units.Comment: 4 pages, 5 figure

Multiple Right-Hand Side Techniques in Semi-Explicit Time Integration Methods for Transient Eddy Current Problems

The spatially discretized magnetic vector potential formulation of magnetoquasistatic field problems is transformed from an infinitely stiff differential algebraic equation system into a finitely stiff ordinary differential equation (ODE) system by application of a generalized Schur complement for nonconducting parts. The ODE can be integrated in time using explicit time integration schemes, e.g. the explicit Euler method. This requires the repeated evaluation of a pseudo-inverse of the discrete curl-curl matrix in nonconducting material by the preconditioned conjugate gradient (PCG) method which forms a multiple right-hand side problem. The subspace projection extrapolation method and proper orthogonal decomposition are compared for the computation of suitable start vectors in each time step for the PCG method which reduce the number of iterations and the overall computational costs.Comment: 4 pages, 5 figure

An Improved Chevron Configuration for the Detection of Magnetic Field Vectors

A modified version of Chevron type Magnetoresistive Recording Heads (MRH) sensor is described. Two shielded ferromagnetic thin-film vertical-type MRH are biased at the linear region simultaneously using a small piece of permanent magnet chip. The biasing rotates the magnetisation vector Ms of each MRH . through 4S· with respect to their respective current vectors J resulting in an effective Chevron orientation of 90·. This configuration is shown to be most effective to detect field vectors in applications such as non-destructive detection of grain structures and loss variation in electrical steels, and in packing more bits of information in magnetic disc storage

Using Local Reduction for the Experimental Evaluation of the Cipher Security

Evaluating the strength of block ciphers against algebraic attacks can be difficult. The attack methods often use different metrics, and experiments do not scale well in practice. We propose a methodology that splits the algebraic attack into a polynomial part (local reduction), and an exponential part (guessing), respectively. The evaluator uses instances with known solutions to estimate the complexity of the attacks, and the response to changing parameters of the problem (e.g. the number of rounds). Although the methodology does not provide a positive answer ("the cipher is secure"), it can be used to construct a negative test (reject weak ciphers), or as a tool of qualitative comparison of cipher designs. Potential applications in other areas of computer science are discussed in the concluding parts of the article

Computational algebraic attacks on the Advanced Encryption Standard (AES)

This thesis examines the vulnerability of the Advanced Encryption Standard (AES) to algebraic attacks. It will explore how strong the Rijndael algorithm must be in order to secure important federal information. There are several algebraic methods of attack that can be used to break a specific cipher, such as Buchburger's and Faugere's F4 and F5 methods. The method to be used and evaluated in this thesis is the Multiple Right Hand Sides (MRHS) Linear Equations. MRHS is a new method that allows computations to be more efficient and the equations to be more compact in comparison with the previously referred methods. Because of the high complexity of the Rijndael algorithm, the purpose of this thesis is to investigate the results of an MRHS attack in a small-scale variant of the AES, since it is impossible to break the actual algorithm by using only the existent knowledge. Instead of the original ten rounds of AES algorithm, variants of up to four rounds were used. Simple examples of deciphering some ciphertexts are presented for different variants of the AES, and the new attack method of MRHS linear equations is compared with the other older methods. This method is more effective timewise than the other older methods, but, in some cases, some systems cannot be uniquely solved.http://archive.org/details/computationallge109454546Hellenic Navy autho

An Optimized Multiple Right-Hand Side Dslash Kernel for Intel Xeon Phi

Lattice quantum chromodynamics (LQCD) stands unique as the only computationally tractable, non-perturbative, and model-independent quantum field theory of the strong nuclear force. The computational core of LQCD is the Wilson Dslash operator, a nearest neighbor stencil operator summing matrix-vector multiplications over lattice points, whose performance is bandwidth-bound on most architectures. Reportedly, up to 90\% of LQCD running time may be spent computing Dslash. In recent years, efforts have been made by researchers to optimize LQCD calculations for floating point coprocessor cards such as GPUs and Intel Xeon Phi Knights Corner (KNC), which boast powerful vector processing units. Most of these efforts in the area of Dslash have focused on single right-hand side solvers. This thesis will present two optimized Dslash kernels which simplify vectorization using multiple right-hand sides and traverse lattices using novel methods. The speedups resulting from these approaches will be explored in the context of KNC\u27s architecture

MRHS Solver Based on Linear Algebra and Exhaustive Search

We show how to build a binary matrix from the MRHS representation of a symmetric-key cipher. The matrix contains the cipher represented as an equation system and can be used to assess a cipher\u27s resistance against algebraic attacks. We give an algorithm for solving the system and compute its complexity. The complexity is normally close to exhaustive search on the variables representing the user-selected key. Finally, we show that for some variants of LowMC, the joined MRHS matrix representation can be used to speed up regular encryption in addition to exhaustive key search

A novel block non-symmetric preconditioner for mixed-hybrid finite-element-based flow simulations

In this work we propose a novel block preconditioner, labelled Explicit Decoupling Factor Approximation (EDFA), to accelerate the convergence of Krylov subspace solvers used to address the sequence of non-symmetric systems of linear equations originating from flow simulations in porous media. The flow model is discretized blending the Mixed Hybrid Finite Element (MHFE) method for Darcy's equation with the Finite Volume (FV) scheme for the mass conservation. The EDFA preconditioner is characterized by two features: the exploitation of the system matrix decoupling factors to recast the Schur complement and their inexact fully-parallel computation by means of restriction operators. We introduce two adaptive techniques aimed at building the restriction operators according to the properties of the system at hand. The proposed block preconditioner has been tested through an extensive experimentation on both synthetic and real-case applications, pointing out its robustness and computational efficiency