It has been shown that the sparse grid combination technique can be a practical tool to solve high dimensional PDEs arising in multidimensional option pricing problems in finance. Hierarchical approximation of these problems leads to linear systems that are smaller in size compared to those arising from standard finite element or finite difference discretizations. However, these systems are still excessively demanding in terms of memory for direct methods and challenging to solve by iterative methods. In this paper we address iterative solutions via preconditioned Krylov subspace based methods, such as Stabilized BiConjugate Gradient (BiCGStab) and CG Squared (CGS), with the main focus on the design of such iterative solvers to harness massive parallelism of general purpose Graphics Processing Units (GPGPU)s. We discuss data structures and efficient implementation of iterative solvers. We also present a number of performance results to demonstrate the scalability of these solvers on the NVIDIA's CUDA platform.
In many numerical applications resulting from computational science and engineering problems, the solution of sparse linear systems is the most prohibitively compute intensive task. Consequently, the linear solvers need to be carefully chosen and efficiently implemented in order to harness the available computing resources. Krylov subspace based iterative solvers have been widely used for solving large systems of linear equations. In this paper, we focus on the design of such iterative solvers to take advantage of massive parallelism of general purpose Graphics Processing Units (GPU)s. We will consider Stabilized BiConjugate Gradient (BiCGStab) and Conjugate Gradient Squared (CGS) methods for the solutions of sparse linear systems with unsymmetric coefficient matrices. We discuss data structures and efficient implementation of these solvers on the NVIDIA's CUDA platform. We evaluate scalability and performance of our implementations in the context of a financial engineering problem of solving multidimensional option pricing PDEs using sparse grid combination technique.Index Terms-Sparse linear iterative solvers, GPU, parallel computing, computational finance.
: Pricing and hedging of higher order derivatives such as multidimensional (up to 100 underlying assets) European and first generation exotic options represent mathematically complex and computationally intensive problems. Grid computing promises to give the capability to handle such intense computations. With several Grid middleware solutions available for gridifying traditional applications, it is cumbersome to select an ideal candidate, to develop financial applications, that can cope up with time critical computational demand for complex pricing requests. In this paper we present SuperQuant Financial Benchmark Suite to evaluate and quantify the overhead imposed by a Grid middleware on throughput of the system and turnaround times for computation. This approach is a step towards producing a middleware independent, reproducible, comparable, self-sufficient and fair performance analysis of Grid middlewares. The result of such performance analysis can be used by middleware vendors to find the bottlenecks and problems in their design and implementation of the system and by financial application developers to verify implementation of their financial algorithms. In this paper we explain the motivation and the details of the proposed benchmark suite. As a proof of concept, we utilize the benchmarks in an International Grid Programming contest and demonstrate the result of initial experiments.
In case of emergency needs the most important lives saver necessity is Blood. Blood Banks are the main providers of blood who receives blood from various donors, monitors the blood groups database of emergencies makes the available to the hospital whenever needed. The major problem faced by the main blood providers and the need is the availability of donor at right time. We hereby took a step forward to build a system to create a network of people who can help each other in need. We propose an application where the Blood banks can timely update the Blood Stock availability and donor and register themselves to donor and user can find blood availability nearby him/her. the urgent time of a blood requirement, user can quickly check for blood banks, hospitals or donor as per requirement matching a particular or related and reach out to them through the App. Application tends to provide list of blood banks in user area. A large number of blood donors are attracted using application. Since almost everyone carries a mobile phone with him, it ensures instant location tracking and communication. Registered user, who is donate blood can pledge him/her to donate and will be able to access the service. In this application we using the GPS technology that will be used to trace the way to the blood bank. The user will get the route to reach the desired location and he/she won't have to ask manually, therefore time can be saved.
This article provides an in-depth overview of thermal heat sink design and optimization. Heat transfer enhancement strategies are discussed in detail, followed by fin design trends and geometries, and a discussion on different fin configurations and their merits is also presented. Important results and findings of experiments concerning the design and optimization of fin geometries have been summarized. For complex heat dissipation applications, researchers have been studying different fin arrangements especially, inclined fins, to maximize the performance of the heat sinks. Along with innovative fin designs, microchannels for heat dissipation are gaining attention due to their. Recent advances in this domain have been discussed. New components are becoming more compact and advanced as a result of technological breakthroughs in electronics and control systems; hence, the use and optimization of heat sinks for modern applications are also discussed in this article.
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