George Gravvanis - Academia.edu (original) (raw)

Papers by George Gravvanis

Research paper thumbnail of Managing Spatial Graph Dependencies in Large Volumes of Traffic Data for Travel-Time Prediction

The exploration of the potential correlations of traffic conditions between roads in large urban ... more The exploration of the potential correlations of traffic conditions between roads in large urban networks, which is of profound importance for achieving accurate traffic prediction, often implies high computational complexity due to the implicated network topology. Hence, focal methods are required for dealing with the urban network complexity, reducing the performance requirements that are associated to the classical network search techniques (e.g., Breadth First Search). This paper introduces a graph-theory-based technique for managing spatial dependence between roads of the same network. In particular, after representing the traffic network as a graph, the local neighbors of each road are extracted using Breadth First Search graph traversal algorithm and a lower complexity variant of it. A Pearson product–moment correlation-coefficient-based metric is applied on the selected graph nodes for a prescribed number of level sets of neighbors. In order to evaluate the impact of the new method to the traffic prediction accuracy achieved, the most correlated roads are used to build a STARIMA model, taking also into account the possible time delays of traffic conditions between the interrelated roads. The proposed technique is benchmarked using traffic data from two different cities: Berlin, Germany, and Thessaloniki, Greece. Benchmark results not only indicate significant improvement on the computational time required for calculating traffic correlation metric values but also reveal that a different variant works better in different network typologies, after comparison to third-party approaches.

Research paper thumbnail of Solving Symmetric Arrowhead and Special Tridiagonal Linear Systems by Fast Approximate Inverse Preconditioning

Journal of Mathematical Modelling and Algorithms, 2002

ABSTRACT

Research paper thumbnail of Explicit Preconditioned Iterative Methods for Solving Large Unsymmetric Finite Element Systems

Computing, 1995

... in-verse of a given banded matrix can be used as an adaptable explicit precondi-tioner for so... more ... in-verse of a given banded matrix can be used as an adaptable explicit precondi-tioner for solving efficiently large ... Note also that the GAIFEM algorithm is explained for a given banded matrix with full bands of uniform size, which ... 3. Explicit Preconditioned Iterative Methods ...

Research paper thumbnail of On numerical modeling performance of generalized preconditioned methods

Proceedings of the 6th Balkan Conference in Informatics on - BCI '13, 2013

ABSTRACT During the last decades, research efforts have been focused on the derivation of effecti... more ABSTRACT During the last decades, research efforts have been focused on the derivation of effective preconditioned iterative methods. The preconditioned iterative methods are mainly categorized into implicit preconditioned methods and explicit preconditioned methods. In this manuscript we review implicit preconditioned methods, based on incomplete and approximate factorization, and explicit preconditioned methods, based on sparse approximate inverses and explicit approximate inverses. Modified Moore-Penrose conditions are presented and theoretical estimates for the sensitivity of the explicit approximate inverse matrix of the explicit preconditioned method are derived. Finally, the performance of the preconditioned iterative methods is illustrated by solving characteristic 2D elliptic problem and numerical results are given indicating a qualitative agreement with the theoretical estimates.

Research paper thumbnail of Explizite Präkonditionierungsverfahren zur Lösung großer unsymmetrischer Finite-Element-Systeme

Research paper thumbnail of Normalized Isomorphic Preconditioned Methods for Solving Sparse Non-Linear Systems

Int. Conf. on Modeling, Simulation & Visualization Methods, 2004

Research paper thumbnail of Parallel preconditioned conjugate gradient square method based on normalized approximate inverses

Scientific Programming, 2005

Research paper thumbnail of Finite Element Approximate Inverse Preconditioning using POSIX threads on multicore systems

International Multiconference on Computer Science and Information Technology - IMCSIT, 2010

Explicit finite element approximate inverse preconditioning methods have been extensively used fo... more Explicit finite element approximate inverse preconditioning methods have been extensively used for solving efficiently sparse linear systems on multiprocessor and multicomputer systems. New parallel computational techniques are proposed for the parallelization of explicit preconditioned biconjugate conjugate gradient type methods, based on Portable Operating System Interface for UniX (POSIX) Threads, for multicore systems. Parallelization is achieved by assigning every loop of

Research paper thumbnail of Performability Evaluation of a Replicated Database System by Explicit Approximate Inverses

Parallel and Distributed Processing Techniques and Applications, 2002

Research paper thumbnail of A Normalized Explicit Preconditioned Conjugate Gradient Method for Solving Sparse Non-linear Systems

Parallel and Distributed Processing Techniques and Applications, 2002

Research paper thumbnail of On the Design of Parallel Finite Element Approximate Inverses

Research paper thumbnail of New Directions in Computing on Demand (CoD)

Today, utility computing and Computing on Demand (CoD) could be parallelized to Grid computing be... more Today, utility computing and Computing on Demand (CoD) could be parallelized to Grid computing because the latter is the best available technology to enable computing power as a massively available utility. In the present paper, iWatt, a naïve linear measurement for CoD services is introduced. The innovative feature of iWatt is considered to be the fact that facilitates both a consumption assignment to a Grid-ready service and a producing capability to CoD infrastructure in an analogous way to electric power device-network interaction. Experimental and benchmarking work need to be done in order to test practical issues for the proposed metric.

Research paper thumbnail of N-body simulation based on the Particle Mesh method using multigrid schemes

Through the last decades multigrid methods have been used extensively in the solution of large sp... more Through the last decades multigrid methods have been used extensively in the solution of large sparse linear systems derived from the discretization of Partial Differential Equations in two or three space variables, subject to a variety of boundary conditions. Due to their efficiency and convergence behavior, multigrid methods are used in many scientific fields as solvers or preconditioners. Herewith, we propose a new algorithm for N-body simulation, based on the V-Cycle multigrid method in conjunction with Generic Approximate SParse Inverses (GenAspI). The N-body problem chosen is in toroidal 3D space and the bodies are subject only to gravitational forces. In each time step, a large sparse linear system is solved to compute the gravity potential at each nodal point in order to interpolate the solution to each body and through the velocity Verlet method compute the new position, velocity and acceleration of each respective body. Moreover, a parallel version of the multigrid algorit...

Research paper thumbnail of Algebraic Multigrid Methods Based on Generic Approximate Banded Inverse Matrix Techniques

Computer Modeling in Engineering and Sciences

Since the introduction of the Algebraic Multi Grid algorithm (AMG) over twenty years ago, signifi... more Since the introduction of the Algebraic Multi Grid algorithm (AMG) over twenty years ago, significant progress has been made in improving the coarsening and the convergence behavior of the method. In this paper, an AMG method is introduced that utilizes a new generic approximate inverse algorithm as a smoother in conjunction with common coarsening techniques, such as classical Ruge-Stuben coarsening, COP and PMIS coarsening. The proposed approximate inverse scheme, namely Generic Approximate Banded Inverse (GenAbI), is a banded approximate inverse based on Incomplete LU factorization with zero fill in (ILU(0)). The new class of Generic Approximate Banded Inverse can be computed for any sparsity pattern of the coefficient matrix, in an analogous way as the explicit approximate inverse, yielding a suitable smoother to be used in conjunction with an Algebraic Multigrid method. The proposed smoother is parameterized and thus by increasing the "retention" parameter the smoothin...

Research paper thumbnail of Schur complement Domain Decomposition in conjunction with Algebraic Multigrid methods based on generic approximate inverses

For decades, Domain Decomposition (DD) techniques have been used for the numerical solution of bo... more For decades, Domain Decomposition (DD) techniques have been used for the numerical solution of boundary value problems. In recent years, the Algebraic Multigrid (AMG) method has also seen significant rise in popularity as well as rapid evolution. In this article, a Domain Decomposition method is presented, based on the Schur complement system and an AMG solver, using generic approximate banded inverses based on incomplete LU factorization. Finally, the applicability and effectiveness of the proposed method on characteristic two dimensional boundary value problems is demonstrated and numerical results on the convergence behavior are given.

Research paper thumbnail of Higher Order Finite Difference Preconditioned Scheme: A Multithreaded Approach

2011 15th Panhellenic Conference on Informatics, 2011

ABSTRACT New parallel computational techniques are introduced for the parallelization of explicit... more ABSTRACT New parallel computational techniques are introduced for the parallelization of explicit finite difference approximate inverse methods, using higher order approximation schemes, based on Portable Operating System Interface for UniX (POSIX) Threads, for multicore systems. Parallelization of the Optimized Banded Generalized Approximate Inverse Finite Element Matrix algorithm is achieved based on the concept of the "fish bone" approach with the use of a thread pool pattern. Theoretical estimates on speedups and efficiency are also presented. Finally, numerical results for the performance of the POBGAIFEM algorithm as well as the loop level and functional level parallelized Explicit Preconditioned Bi-conjugate Gradient Gradient-STAB method for solving two dimensional boundary value problems on multicore computer systems are presented.

Research paper thumbnail of A Note on the Comparison of a Class of Preconditioned Iterative Methods

2012 16th Panhellenic Conference on Informatics, 2012

ABSTRACT The preconditioned iterative methods are mainly categorized into implicit preconditioned... more ABSTRACT The preconditioned iterative methods are mainly categorized into implicit preconditioned methods and explicit preconditioned methods. In this manuscript we review implicit preconditioned methods, based on incomplete and approximate factorization, and explicit preconditioned methods, based on sparse approximate inverses and explicit approximate inverses. Additionally we present the modified Moore-Penrose conditions and theoretical estimates on the iteration matrix of the explicit preconditioned method, based on explicit approximate inverses. Finally, the performance of the preconditioned iterative methods is illustrated by solving characteristic 2D elliptic problem and numerical results are given. The theoretical estimates were in qualitative agreement with the numerical results.

Research paper thumbnail of On the Algebraic Multigrid Method Based on Generic Approximate Banded Inverses

2012 16th Panhellenic Conference on Informatics, 2012

ABSTRACT Since the introduction of the Algebraic MultiGrid algorithm (AMG) over twenty years ago,... more ABSTRACT Since the introduction of the Algebraic MultiGrid algorithm (AMG) over twenty years ago, significant progress has been made in improving and refining it. In this article, an AMG method is presented using generic approximate banded inverses based on incomplete LU factorization as smoothers. Finally, the applicability and effectiveness of the proposed AMG method on a characteristic two dimensional boundary value problem is demonstrated and numerical results on the convergence behavior and convergence factor are given.

Research paper thumbnail of Distributed Generation Influence on a Network Voltage Profile

In this article the voltage profile of a power distribution network under high distributed genera... more In this article the voltage profile of a power distribution network under high distributed generation penetration is examined. Previous research performed at the Power Systems Laboratory of the Electrical and Computer Engineering Department, Democritus University Thrace, has indicated that voltage drop instead of the expected voltage rise appears, when large amount of embedded generation is connected to the electrical grid. The above finding is studied here, both through a two bus grid model and a real medium voltage power distribution network. In the simplified grid, the analytical mathematical equations concerning the bus voltages were derived and implemented in the MATLAB software environment in order to reach an initial approach of this voltage turning point and the parameters that affect it. The derivation of the analytical solution of the problem is complicated even for the above simplified network. For this reason, parametrical investigations related to the buses voltage prof...

Research paper thumbnail of Performance analysis of an electrical substation via Semi Markov process computed by generalized approximate inverse preconditioning

An electrical substation is simulated by a Semi Markov process model and a performability indicat... more An electrical substation is simulated by a Semi Markov process model and a performability indicator was computed in order to estimate asymptotically the amount of the mean energy not supplied due to different maintenance policies. Additionally, the same study was performed by a Homogeneous Markov process in order to compare the results. Moreover, the steady state probabilities were computed by solving a sparse linear system of algebraic equations, using generalized explicit approximate inverse preconditioning methods.

Research paper thumbnail of Managing Spatial Graph Dependencies in Large Volumes of Traffic Data for Travel-Time Prediction

The exploration of the potential correlations of traffic conditions between roads in large urban ... more The exploration of the potential correlations of traffic conditions between roads in large urban networks, which is of profound importance for achieving accurate traffic prediction, often implies high computational complexity due to the implicated network topology. Hence, focal methods are required for dealing with the urban network complexity, reducing the performance requirements that are associated to the classical network search techniques (e.g., Breadth First Search). This paper introduces a graph-theory-based technique for managing spatial dependence between roads of the same network. In particular, after representing the traffic network as a graph, the local neighbors of each road are extracted using Breadth First Search graph traversal algorithm and a lower complexity variant of it. A Pearson product–moment correlation-coefficient-based metric is applied on the selected graph nodes for a prescribed number of level sets of neighbors. In order to evaluate the impact of the new method to the traffic prediction accuracy achieved, the most correlated roads are used to build a STARIMA model, taking also into account the possible time delays of traffic conditions between the interrelated roads. The proposed technique is benchmarked using traffic data from two different cities: Berlin, Germany, and Thessaloniki, Greece. Benchmark results not only indicate significant improvement on the computational time required for calculating traffic correlation metric values but also reveal that a different variant works better in different network typologies, after comparison to third-party approaches.

Research paper thumbnail of Solving Symmetric Arrowhead and Special Tridiagonal Linear Systems by Fast Approximate Inverse Preconditioning

Journal of Mathematical Modelling and Algorithms, 2002

ABSTRACT

Research paper thumbnail of Explicit Preconditioned Iterative Methods for Solving Large Unsymmetric Finite Element Systems

Computing, 1995

... in-verse of a given banded matrix can be used as an adaptable explicit precondi-tioner for so... more ... in-verse of a given banded matrix can be used as an adaptable explicit precondi-tioner for solving efficiently large ... Note also that the GAIFEM algorithm is explained for a given banded matrix with full bands of uniform size, which ... 3. Explicit Preconditioned Iterative Methods ...

Research paper thumbnail of On numerical modeling performance of generalized preconditioned methods

Proceedings of the 6th Balkan Conference in Informatics on - BCI '13, 2013

ABSTRACT During the last decades, research efforts have been focused on the derivation of effecti... more ABSTRACT During the last decades, research efforts have been focused on the derivation of effective preconditioned iterative methods. The preconditioned iterative methods are mainly categorized into implicit preconditioned methods and explicit preconditioned methods. In this manuscript we review implicit preconditioned methods, based on incomplete and approximate factorization, and explicit preconditioned methods, based on sparse approximate inverses and explicit approximate inverses. Modified Moore-Penrose conditions are presented and theoretical estimates for the sensitivity of the explicit approximate inverse matrix of the explicit preconditioned method are derived. Finally, the performance of the preconditioned iterative methods is illustrated by solving characteristic 2D elliptic problem and numerical results are given indicating a qualitative agreement with the theoretical estimates.

Research paper thumbnail of Explizite Präkonditionierungsverfahren zur Lösung großer unsymmetrischer Finite-Element-Systeme

Research paper thumbnail of Normalized Isomorphic Preconditioned Methods for Solving Sparse Non-Linear Systems

Int. Conf. on Modeling, Simulation & Visualization Methods, 2004

Research paper thumbnail of Parallel preconditioned conjugate gradient square method based on normalized approximate inverses

Scientific Programming, 2005

Research paper thumbnail of Finite Element Approximate Inverse Preconditioning using POSIX threads on multicore systems

International Multiconference on Computer Science and Information Technology - IMCSIT, 2010

Explicit finite element approximate inverse preconditioning methods have been extensively used fo... more Explicit finite element approximate inverse preconditioning methods have been extensively used for solving efficiently sparse linear systems on multiprocessor and multicomputer systems. New parallel computational techniques are proposed for the parallelization of explicit preconditioned biconjugate conjugate gradient type methods, based on Portable Operating System Interface for UniX (POSIX) Threads, for multicore systems. Parallelization is achieved by assigning every loop of

Research paper thumbnail of Performability Evaluation of a Replicated Database System by Explicit Approximate Inverses

Parallel and Distributed Processing Techniques and Applications, 2002

Research paper thumbnail of A Normalized Explicit Preconditioned Conjugate Gradient Method for Solving Sparse Non-linear Systems

Parallel and Distributed Processing Techniques and Applications, 2002

Research paper thumbnail of On the Design of Parallel Finite Element Approximate Inverses

Research paper thumbnail of New Directions in Computing on Demand (CoD)

Today, utility computing and Computing on Demand (CoD) could be parallelized to Grid computing be... more Today, utility computing and Computing on Demand (CoD) could be parallelized to Grid computing because the latter is the best available technology to enable computing power as a massively available utility. In the present paper, iWatt, a naïve linear measurement for CoD services is introduced. The innovative feature of iWatt is considered to be the fact that facilitates both a consumption assignment to a Grid-ready service and a producing capability to CoD infrastructure in an analogous way to electric power device-network interaction. Experimental and benchmarking work need to be done in order to test practical issues for the proposed metric.

Research paper thumbnail of N-body simulation based on the Particle Mesh method using multigrid schemes

Through the last decades multigrid methods have been used extensively in the solution of large sp... more Through the last decades multigrid methods have been used extensively in the solution of large sparse linear systems derived from the discretization of Partial Differential Equations in two or three space variables, subject to a variety of boundary conditions. Due to their efficiency and convergence behavior, multigrid methods are used in many scientific fields as solvers or preconditioners. Herewith, we propose a new algorithm for N-body simulation, based on the V-Cycle multigrid method in conjunction with Generic Approximate SParse Inverses (GenAspI). The N-body problem chosen is in toroidal 3D space and the bodies are subject only to gravitational forces. In each time step, a large sparse linear system is solved to compute the gravity potential at each nodal point in order to interpolate the solution to each body and through the velocity Verlet method compute the new position, velocity and acceleration of each respective body. Moreover, a parallel version of the multigrid algorit...

Research paper thumbnail of Algebraic Multigrid Methods Based on Generic Approximate Banded Inverse Matrix Techniques

Computer Modeling in Engineering and Sciences

Since the introduction of the Algebraic Multi Grid algorithm (AMG) over twenty years ago, signifi... more Since the introduction of the Algebraic Multi Grid algorithm (AMG) over twenty years ago, significant progress has been made in improving the coarsening and the convergence behavior of the method. In this paper, an AMG method is introduced that utilizes a new generic approximate inverse algorithm as a smoother in conjunction with common coarsening techniques, such as classical Ruge-Stuben coarsening, COP and PMIS coarsening. The proposed approximate inverse scheme, namely Generic Approximate Banded Inverse (GenAbI), is a banded approximate inverse based on Incomplete LU factorization with zero fill in (ILU(0)). The new class of Generic Approximate Banded Inverse can be computed for any sparsity pattern of the coefficient matrix, in an analogous way as the explicit approximate inverse, yielding a suitable smoother to be used in conjunction with an Algebraic Multigrid method. The proposed smoother is parameterized and thus by increasing the "retention" parameter the smoothin...

Research paper thumbnail of Schur complement Domain Decomposition in conjunction with Algebraic Multigrid methods based on generic approximate inverses

For decades, Domain Decomposition (DD) techniques have been used for the numerical solution of bo... more For decades, Domain Decomposition (DD) techniques have been used for the numerical solution of boundary value problems. In recent years, the Algebraic Multigrid (AMG) method has also seen significant rise in popularity as well as rapid evolution. In this article, a Domain Decomposition method is presented, based on the Schur complement system and an AMG solver, using generic approximate banded inverses based on incomplete LU factorization. Finally, the applicability and effectiveness of the proposed method on characteristic two dimensional boundary value problems is demonstrated and numerical results on the convergence behavior are given.

Research paper thumbnail of Higher Order Finite Difference Preconditioned Scheme: A Multithreaded Approach

2011 15th Panhellenic Conference on Informatics, 2011

ABSTRACT New parallel computational techniques are introduced for the parallelization of explicit... more ABSTRACT New parallel computational techniques are introduced for the parallelization of explicit finite difference approximate inverse methods, using higher order approximation schemes, based on Portable Operating System Interface for UniX (POSIX) Threads, for multicore systems. Parallelization of the Optimized Banded Generalized Approximate Inverse Finite Element Matrix algorithm is achieved based on the concept of the "fish bone" approach with the use of a thread pool pattern. Theoretical estimates on speedups and efficiency are also presented. Finally, numerical results for the performance of the POBGAIFEM algorithm as well as the loop level and functional level parallelized Explicit Preconditioned Bi-conjugate Gradient Gradient-STAB method for solving two dimensional boundary value problems on multicore computer systems are presented.

Research paper thumbnail of A Note on the Comparison of a Class of Preconditioned Iterative Methods

2012 16th Panhellenic Conference on Informatics, 2012

ABSTRACT The preconditioned iterative methods are mainly categorized into implicit preconditioned... more ABSTRACT The preconditioned iterative methods are mainly categorized into implicit preconditioned methods and explicit preconditioned methods. In this manuscript we review implicit preconditioned methods, based on incomplete and approximate factorization, and explicit preconditioned methods, based on sparse approximate inverses and explicit approximate inverses. Additionally we present the modified Moore-Penrose conditions and theoretical estimates on the iteration matrix of the explicit preconditioned method, based on explicit approximate inverses. Finally, the performance of the preconditioned iterative methods is illustrated by solving characteristic 2D elliptic problem and numerical results are given. The theoretical estimates were in qualitative agreement with the numerical results.

Research paper thumbnail of On the Algebraic Multigrid Method Based on Generic Approximate Banded Inverses

2012 16th Panhellenic Conference on Informatics, 2012

ABSTRACT Since the introduction of the Algebraic MultiGrid algorithm (AMG) over twenty years ago,... more ABSTRACT Since the introduction of the Algebraic MultiGrid algorithm (AMG) over twenty years ago, significant progress has been made in improving and refining it. In this article, an AMG method is presented using generic approximate banded inverses based on incomplete LU factorization as smoothers. Finally, the applicability and effectiveness of the proposed AMG method on a characteristic two dimensional boundary value problem is demonstrated and numerical results on the convergence behavior and convergence factor are given.

Research paper thumbnail of Distributed Generation Influence on a Network Voltage Profile

In this article the voltage profile of a power distribution network under high distributed genera... more In this article the voltage profile of a power distribution network under high distributed generation penetration is examined. Previous research performed at the Power Systems Laboratory of the Electrical and Computer Engineering Department, Democritus University Thrace, has indicated that voltage drop instead of the expected voltage rise appears, when large amount of embedded generation is connected to the electrical grid. The above finding is studied here, both through a two bus grid model and a real medium voltage power distribution network. In the simplified grid, the analytical mathematical equations concerning the bus voltages were derived and implemented in the MATLAB software environment in order to reach an initial approach of this voltage turning point and the parameters that affect it. The derivation of the analytical solution of the problem is complicated even for the above simplified network. For this reason, parametrical investigations related to the buses voltage prof...

Research paper thumbnail of Performance analysis of an electrical substation via Semi Markov process computed by generalized approximate inverse preconditioning

An electrical substation is simulated by a Semi Markov process model and a performability indicat... more An electrical substation is simulated by a Semi Markov process model and a performability indicator was computed in order to estimate asymptotically the amount of the mean energy not supplied due to different maintenance policies. Additionally, the same study was performed by a Homogeneous Markov process in order to compare the results. Moreover, the steady state probabilities were computed by solving a sparse linear system of algebraic equations, using generalized explicit approximate inverse preconditioning methods.