Iterative Method

For an edge-weighted connected undirected graph, the minimum k-way cut problem is to find a subset of edges of minimum total weight whose removal separates the graph into k connected components. The problem is NP-hard when k is part of the input and W[1]-hard when k is taken as a parameter. A simple algorithm for approximating a minimum k-way cut

Solving linear system with a magnitude of thousand to ten thousand of unknowns takes a very long time in serial fashion. Furthermore, linear system that is discretised from Partial Differentiation Equations (PDE) is also typically solved by a class of iterative method. Therefore, by parallelising Jacobi Iterative Method using OpenACC, we are able to review and compare OpenACC’s capabilities in accelerating Jacobi Iterative Method using compiler directives approach as opposed to CUDA’s approach. Moreover, we implemented OpenACC in two distinctive domains, where the first domain is on manycore environment with a testbed hardware of Nvidia GeForce GTX 980 and the second domain is on multicore environment where 4 CPU(s) of AMD Opteron 6272 chips are clustered on a single machine with a total of 64 cores. This research project has shown great potentials of the implemented Jacobi Iterative Method using OpenACC as we managed to obtain verily rewarding results. Where, the highest speedup gain is up to 82x faster on GPU with Unified Memory (UM) enabled and 55x times faster on CPU where all 64 cores are fully utilized, and this is when the number of unknowns to be solved is 25,000 and 2,500 respectively.

This paper describes a method developed to evaluate the seismic performance of old masonry buildings, which allows identifying the expected structural collapse mechanism of the structure. The collapse mechanism is identified by the accumulation of several damaged ...

In this paper, we have combined the ideas of the False Position (FP) and Artificial Bee Colony (ABC) algorithms to find a fast and novel method for solving nonlinear equations. Additionally, to illustrate the efficiency of the proposed method, several benchmark functions are solved and compared with other methods such as ABC, PSO and GA.

For an edge-weighted connected undirected graph, the minimum k-way cut problem is to find a subset of edges of minimum total weight whose removal separates the graph into k connected components. The problem is NP-hard when k is part of the input and W[1]-hard when k is taken as a parameter. A simple algorithm for approximating a minimum k-way cut

This paper is concerned with a compact finite difference method for solving systems of two-dimensional reaction–diffusion equations. This method has the accuracy of fourth-order in both space and time. The existence and uniqueness of the finite difference solution are investigated by the method of upper and lower solutions, without any monotone requirement on the nonlinear term. Three monotone iterative algorithms

For an edge-weighted connected undirected graph, the minimum k-way cut problem is to find a subset of edges of minimum total weight whose removal separates the graph into k connected components. The problem is NP-hard when k is part of the input and W[1]-hard when k is taken as a parameter. A simple algorithm for approximating a minimum k-way cut

This article describes recent technical developments that have made the total-energy pseudopotential the most powerful {ital ab} {ital initio} quantum-mechanical modeling method presently available. In addition to presenting technical details of the pseudopotential method, the article aims to heighten awareness of the capabilities of the method in order to stimulate its application to as wide a range of problems in