Big data simulation software for breast cancer growth repository system

The development of the simulation software aims at anticipating the growth of breast cancer. Based on certain numerical iterative methods, this simulation works with discretization and Partial Differential Equation (PDE). As a class of Helmholtz equations, PDE approach are known to govern the growth of this type of cancer. Considering both time and place, the Helmholtz equation’s accuracy visualizes breast cancer and its growth. This growth is of breast cancer is captured and the convergence results in sequential and parallel computing environment is expressed through the numerical libraries available in the repository system. Currently, both the parallel performance measurement and Numerical analysis that involve execution time, speedup, efficiency, effectiveness and temporal performance are being investigated. The process of breast cancer visualization requires a huge memory and expensive calculations. It is observed that both the distributed memory and distributed processors of the parallel computer systems development were required in most of the studies conducted on the growth of this cancer. It is considered as an important computation platform needed to the development of parallel repository system leading to an increase in the speed and a decrease in the cost. The simulation software has several beneficial characteristics such as high performance estimation, multidimensional visualization of breast cancer and being friendly. It also provides a real time solution and strength. This soft-ware is expected to increase the level of confidence in terms of computer-aided decision making which can be reflected positively on comprehensive breast cancer screening; breast cancer diagnosis; and clinical assessments and treatment

The AGE iterative methods for solving large linear systems occurring in differential equations

The work presented in this thesis is wholly concerned with the Alternating Group Explicit (AGE) iterative methods for solving large linear systems occurring in solving Ordinary and Partial Differential Equations (ODEs and PDEs) using finite difference approximations. [Continues.

Tensor Numerical Methods in Quantum Chemistry: from Hartree-Fock Energy to Excited States

We resume the recent successes of the grid-based tensor numerical methods and discuss their prospects in real-space electronic structure calculations. These methods, based on the low-rank representation of the multidimensional functions and integral operators, led to entirely grid-based tensor-structured 3D Hartree-Fock eigenvalue solver. It benefits from tensor calculation of the core Hamiltonian and two-electron integrals (TEI) in $O(n\log n)$ complexity using the rank-structured approximation of basis functions, electron densities and convolution integral operators all represented on 3D $n\times n\times n$ Cartesian grids. The algorithm for calculating TEI tensor in a form of the Cholesky decomposition is based on multiple factorizations using algebraic 1D ``density fitting`` scheme. The basis functions are not restricted to separable Gaussians, since the analytical integration is substituted by high-precision tensor-structured numerical quadratures. The tensor approaches to post-Hartree-Fock calculations for the MP2 energy correction and for the Bethe-Salpeter excited states, based on using low-rank factorizations and the reduced basis method, were recently introduced. Another direction is related to the recent attempts to develop a tensor-based Hartree-Fock numerical scheme for finite lattice-structured systems, where one of the numerical challenges is the summation of electrostatic potentials of a large number of nuclei. The 3D grid-based tensor method for calculation of a potential sum on a $L\times L\times L$ lattice manifests the linear in $L$ computational work, $O(L)$, instead of the usual $O(L^3 \log L)$ scaling by the Ewald-type approaches

Frequency Domain Ultrasound Waveform Tomography Breast Imaging

Ultrasound tomography is an emerging modality for imaging breast tissue for the detection of disease. Using the principles of full waveform inversion, high-resolution quantitative sound speed and attenuation maps of the breast can be created. In this thesis, we introduce some basic principles of imaging breast disease and the formalism of sound wave propagation. We present numerical methods to model acoustic wave propagation as well methods to solve the corresponding inverse problem. Numerical simulations of sound speed and attenuation reconstructions are used to assess the efficacy of the algorithm. A careful review of the preprocessing techniques needed for the successful inversion of acoustic data is presented. Ex vivo and in vivo sound speed reconstructions highlight the significant improvements that are made upon commonly used travel time sound speed reconstruction methods. Note that we do not present ex vivo or in vivo attenuation reconstructions in this thesis. For the sound speed images, the higher resolution and contrast of the waveform method will hopefully allow a radiologist to make a more informed diagnosis of breast disease. A comparison of full waveform sound speed imaging to MRI shows a great deal of concordant findings. Lastly, we give examples of the use of full waveform inversion sound speed imaging in a clinical setting

Parallelization of multidimensional hyperbolic partial differential equation on détente instantanée contrôlée dehydration process

The purpose of this research is to propose some new modified mathematical models to enhance the previous model in simulating, visualizing and predicting the heat and mass transfer in dehydration process using instant controlled pressure drop (DIC) technique. The main contribution of this research is the mathematical models which are formulated from the regression model (Haddad et al., 2007) to multidimensional hyperbolic partial differential equation (HPDE) involving dependent parameters; moisture content, temperature, and pressure, and independent parameters; time and dimension of region. The HPDE model is performed in multidimensional; one, two and three dimensions using finite difference method with central difference formula is used to discretize the mathematical models. The implementation of numerical methods such as Alternating Group Explicit with Brian (AGEB) and Douglas-Rachford (AGED) variances, Red Black Gauss Seidel (RBGS) and Jacobi (JB) method to solve the system of linear equation is another contribution of this research. The sequential algorithm is developed by using Matlab R2011a software. The numerical results are analyzed based on execution time, number of iterations, maximum error, root mean square error, and computational complexity. The grid generation process involved a fine grained large sparse data by minimizing the size of interval, increasing the dimension of the model and level of time steps. Another contribution is the implementation of the parallel algorithm to increase the speedup of computation and to reduce computational complexity problem. The parallelization of the mathematical model is run on Matlab Distributed Computing Server with Linux operating system. The parallel performance evaluation of multidimensional simulation in terms of execution time, speedup, efficiency, effectiveness, temporal performance, granularity, computational complexity and communication cost are analyzed for the performance of parallel algorithm. As a conclusion, the thesis proved that the multidimensional HPDE is able to be parallelized and PAGEB method is the alternative solution for the large sparse simulation. Based on the numerical results and parallel performance evaluations, the parallel algorithm is able to reduce the execution time and computational complexity compared to the sequential algorithm

BTEC Thermal Model

AFRL/RHDO has developed a configurable, laser-tissue interaction model that includes components from various areas of Biophysics. The model predicts heat transfer in biological tissue, in either one-dimension or two-dimensional cylindrical coordinates, and is coupled to an Arrhenius damage model. A simulation can be configured as a single run, or a damage-threshold search. Multiple models for describing the laser-tissue interaction are available, including linear absorption (1D, 2D), Monte Carlo scattering (2D) and Beam Propagation Methods using Finite Difference approximations or Hankel Transform methods (2D)

Planar inviscid flows in a channel of finite length : washout, trapping and self-oscillations of vorticity

The paper addresses the nonlinear dynamics of planar inviscid incompressible flows in the straight channel of a finite length. Our attention is focused on the effects of boundary conditions on vorticity dynamics. The renowned Yudovich's boundary conditions (YBC) are the normal component of velocity given at all boundaries, while vorticity is prescribed at an inlet only. The YBC are fully justified mathematically: the well posedness of the problem is proven. In this paper we study general nonlinear properties of channel flows with YBC. There are 10 main results in this paper: (i) the trapping phenomenon of a point vortex has been discovered, explained and generalized to continuously distributed vorticity such as vortex patches and harmonic perturbations; (ii) the conditions sufficient for decreasing Arnold's and enstrophy functionals have been found, these conditions lead us to the washout property of channel flows; (iii) we have shown that only YBC provide the decrease of Arnold's functional; (iv) three criteria of nonlinear stability of steady channel flows have been formulated and proven; (v) the counterbalance between the washout and trapping has been recognized as the main factor in the dynamics of vorticity; (vi) a physical analogy between the properties of inviscid channel flows with YBC, viscous flows and dissipative dynamical systems has been proposed; (vii) this analogy allows us to formulate two major conjectures (C1 and C2) which are related to the relaxation of arbitrary initial data to C1: steady flows, and C2: steady, self-oscillating or chaotic flows; (viii) a sufficient condition for the complete washout of fluid particles has been established; (ix) the nonlinear asymptotic stability of selected steady flows is proven and the related thresholds have been evaluated; (x) computational solutions that clarify C1 and C2 and discover three qualitatively different scenarios of flow relaxation have been obtained