AUTOMATION OF CONSTRUCTION OF A SCHEME FOR SOLVING COMPUTE- INTENSIVE PROBLEMS OF MATHEMATICAL PHYSICS ON SUPERCOMPUTERS

В статье представлен подход к разработке информационно-аналитической системы, помогающей исследователю решать вычислительно сложные задачи математической физики на суперкомпьютерах. Система автоматически строит схему решения задачи по спецификации пользователя, введенной им в режиме диалога. Схема включает наиболее подходящие математические модели для решения задачи, численные методы, алгоритмы и параллельные архитектуры, ссылки на доступные фрагменты параллельного кода, которые пользователь может использовать при разработке собственного кода. Построение схемы осуществляется на основе онтологии проблемной области «Решение вычислительно сложных задач математической физики», онтологии заданной предметной области и экспертных правил, построенных с использованием технологии Semantic Web. The paper presents an approach to the development of an information-analytical system that helps a researcher to solve compute-intensive problems of mathematical physics on supercomputers. The system automatically builds a scheme for solving the problem according to the user's specification entered by him in the dialogue mode. The scheme includes the most suitable mathematical models for solving the problem, numerical methods, algorithms and parallel architectures, links to available fragments of parallel code that the user can use when developing their own code. The construction of the scheme is carried out on the basis of the ontology of the problem area "Solving compute-intensive problems of mathematical physics", the ontology of a given subject area and expert rules built using the Semantic Web technology.

The automated construction of a scheme for solving compute-intensive problems based on the ontological approach and Semantic Web technologies

This paper describes the tools for supporting researchers in the development of a parallel code. The tools are based on the ontology of the knowledge area “Support for solving compute-intensive problems of mathematical physics on supercomputers”. The main result of these tools operation is a scheme for solving the problem, built according to its specification provided by the user. The scheme includes the most suitable mathematical models for solving the problem, numerical methods, algorithms, and parallel architectures, links to available fragments of a parallel code that the user can use when developing his own code. The scheme construction is carried out on the basis of ontology and expert rules built using the Semantic Web technology.

Parallel Tiled Code for Computing General Linear Recurrence Equations

In this article, we present a technique that allows us to generate parallel tiled code to calculate general linear recursion equations (GLRE). That code deals with multidimensional data and it is computing-intensive. We demonstrate that data dependencies available in an original code computing GLREs do not allow us to generate any parallel code because there is only one solution to the time partition constraints built for that program. We show how to transform the original code to another one that exposes dependencies such that there are two linear distinct solutions to the time partition restrictions derived from these dependencies. This allows us to generate parallel 2D tiled code computing GLREs. The wavefront technique is used to achieve parallelism, and the generated code conforms to the OpenMP C/C++ standard. The experiments that we conducted with the resulting parallel 2D tiled code show that this code is much more efficient than the original serial code computing GLREs. Code performance improvement is achieved by allowing parallelism and better locality of the target code.

Restoration of Legacy Parallelism: Transforming Pthreads into Farm and Pipeline Patterns

Parallel patterns are a high-level programming paradigm that enables non-experts in parallelism to develop structured parallel programs that are maintainable, adaptive, and portable whilst achieving good performance on a variety of parallel systems. However, there still exists a large base of legacy-parallel code developed using ad-hoc methods and incorporating low-level parallel/concurrency libraries such as pthreads without any parallel patterns in the fundamental design. This code would benefit from being restructured and rewritten into pattern-based code. However, the process of rewriting the code is laborious and error-prone, due to typical concurrency and pthreading code being closely intertwined throughout the business logic of the program. In this paper, we present a new software restoration methodology, to transform legacy-parallel programs implemented using pthreads into structured farm and pipeline patterned equivalents. We demonstrate our restoration technique on a number of benchmarks, allowing the introduction of patterned farm and pipeline parallelism in the resulting code; we record improvements in cyclomatic complexity and speedups on a number of representative benchmarks.

Expressing Parallelism

Now we can put together our first collection of puzzle pieces. We already know how to place code (Chapter 10.1007/978-1-4842-5574-2_2) and data (Chapter 10.1007/978-1-4842-5574-2_3) on a device—all we must do now is engage in the art of deciding what to do with it. To that end, we now shift to fill in a few things that we have conveniently left out or glossed over so far. This chapter marks the transition from simple teaching examples toward real-world parallel code and expands upon details of the code samples we have casually shown in prior chapters.

GPU COMPUTING FOR 2D WAVE EQUATION BASED ON IMPLICIT FINITE DIFFERENCE SCHEMES

In this paper we will consider the numerical implementation of the 2d wave equation which is a fundamental equation in many engineering problems. An approximate solution of a function is calculated from discrete points in spatial grid based on discrete time steps. The initial values are given by the initial value condition. First we will interpret how to transform a differential equation into an implicit finitedifference equation, respectively, a set of finite-difference equations that can be used to calculate an approximate solution. Then we will change this algorithm to parallelize this task on GPU. Special focus is on improving the performance of the parallel algorithm. In addition, we will run the implemented parallel code on the GPU and serial code the central processor, calculate the acceleration based on the execution time. We present that the parallel code that runs on a GPU gives the expected results by comparing our results to those obtained by running serial code of the same simulation on the CPU. In fact, in some cases, simulations on the GPU are found to run 22 times faster than on a CPU