NumAn2014 Proceedings
http://lib.amcl.tuc.gr/handle/triton/15
Proceedings of the 6th International Conference on Numerical Analysis (NumAn2014)2018-10-19T04:42:22ZThe Unified Transfrom Technique for Linear Elliptic PDEs in a Square Domain
http://lib.amcl.tuc.gr/handle/triton/71
The Unified Transfrom Technique for Linear Elliptic PDEs in a Square Domain
Hashemzadeh, P.; Fokas, Athanassios S.
For linear elliptic PDEs formulated in the interior of a polygon, the socalled unified transform (or Fokas method) gives rise to a novel numerical technique. This technique, which can be considered as the counterpart in the complex Fourier plane of the well known boundary integral method which is formulated in the physical plane, is illustrated for the simple cases of the Laplace, modified Helmholtz and Helmholtz equations formulated in the interior of a square.
2014-09-02T00:00:00ZCPU-GPU computations for MultiGrid techniques coupled with Fourth-Order Compact Discretizations for Isotropic and Anisotropic Poisson problems
http://lib.amcl.tuc.gr/handle/triton/70
CPU-GPU computations for MultiGrid techniques coupled with Fourth-Order Compact Discretizations for Isotropic and Anisotropic Poisson problems
Charalampaki, Niki E.; Mathioudakis, Emmanuel N.
A CPU-GPU parallel algorithm for a fourth-order compact finite difference scheme with unequal mesh size in different coordinate directions, is designed to discretize a two dimensional isotropic or anisotropic Poisson equation in a rectangular domain. A multigrid technique with partial semi-coarsening strategy is used to iteratively solve the sparse linear system derived. Numbering the unknowns and equations according to the line red-black fashion, the coefficient matrix obtains a block structure suitable for parallel computations. These blocks consist of symmetric tridiagonal matrices allowing the efficient solution of inner linear systems on parallel computing environments with accelerators. The realization of the algorithm takes place on a HP SL390s G7 multicore system with Tesla M2070 GPUs and the application is developed in double precision Fortran code using the OpenACC standard with PGI’s compilers. The performance investigation reveals that the solution of fine discretization problems can be accelerated, although multigrid techniques usually yield poor efficiency on parallel computing architectures due to solution approximations of decreased size problems.
2014-09-02T00:00:00ZA multigrid accelerated high-order pressure correction compact scheme for incompressible Navier-Stokes solvers
http://lib.amcl.tuc.gr/handle/triton/69
A multigrid accelerated high-order pressure correction compact scheme for incompressible Navier-Stokes solvers
Mandikas, Vassilios G.; Mathioudakis, Emmanuel N.; Kozyrakis, G. V.; Ekaterinaris, John A.; Kampanis, Nikolaos A.
A high-order accurate compact finite-difference numerical scheme, based on multigrid techniques, is constructed on staggered grids in order to develop an efficient incompressible Navier-Stokes solver. The enforcement of the incompressibility condition by solving a Poisson-type equation at each time step is commonly accepted to be the most computationally demanding part of the global pressure correction procedure of a numerical method. Since the efficiency of the overall algorithm depends on the Poisson solver, a multigrid acceleration technique coupled with compact high-order descretization scheme is implemented to accelerate the iterative procedure of the pressure updates and enhance computational efficiency. The employment of geometric multigrid techniques on staggered grids has an intrinsic difficulty, since the coarse grids do not constitute part of the finer grids. Appropriate boundary closure formulas are developed for the cell-centered pressure approximations of the boundary conditions. Performance investigations demonstrate that the proposed multigrid algorithm can significantly accelerate the numerical solution process, while retaining the high order of accuracy of the numerical method even for high Reynolds number flows.
2014-09-02T00:00:00ZAn extended method for robust image registration
http://lib.amcl.tuc.gr/handle/triton/68
An extended method for robust image registration
Spanakis, Constantinus; Marias, K.; Mathioudakis, Emmanuel N.; Kampanis, Nikolaos A.
Image Registration is the process of transforming sets of data acquired at different time-points, sensors and viewpoints into a single coordinate system. It is widely used in computer vision, medical imaging and satellite image analysis. Although it has been a central research topic in computer vision and medical image analysis for a long time, there are still unresolved issues and success rates seem to be data-dependent. There are many categories of methods that that are able to align images, but usually they are either specialized and accurate for specific types of data or more generic and error-prone, frequently stumbling upon pitfalls. In this work, we present our implementation and results on Maes’ method[1]. By using three different variants of mutual information (used as the similarity measure), we present indicative results from different imaging domains and discuss the drawbacks/pitfalls of the method especially with regard to initial transformation selection and the initial direction vectors. Different starting point or/and different initial direction vectors may lead to different “optimal” alignment registration results which very often are erroneous. In order to solve this problem, we propose an extension of this method by enhancing its global optimization scheme by means of stochastic optimization.
2014-09-02T00:00:00Z