Engaging in High Performance Computing library optimization research. Supporting HPC community formation of FFT library.
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نخطط هنا لتحسين تطبيق تحويلات فورييه السريع (إف إف تي) على تصميمات بناء اجهزة الحوسبة عالية الأداء المستجدة، وحشد المجتمع الدولي من الخبراء لقياسه بجهودنا وجهودهم، للوصول الى اعتماد تكنولوجية برمجيات (إف إف تي) التي هي الأسرع والأكثر كفاءة. هناك حاجة لا حصر لها لأجهزة الكمبيوتر التي يمكن أن تحسن التنبؤ العلمي والتصميم الهندسي من خلال زيادة الدقة ( بزيادة الذاكرة) وتقليل مرات التنفيذ (بالاكثار من المعالجات المتزامنة) مع متطلبات طاقة أقل (تكون أكثر ملاءمة للبيئة وأوفر إقتصاديا). حدود السرعة المقبلة لكل من خصائص بناء اجهزة الحوسبة العالية الأداء الثلاثة السابقة هي سرعة الإكساسكيل أي ١٠**١٥ عملية في الثانية بحدود ١٠**١٥ كلمة في الذاكرة. تحويل فورييه السريع (إف إف تي) هو لبنة بناء أساسية للخوارزميات في العلوم الحاسوبية والهندسة. وله تعقيدات تشغيلية تنمو بشكل أسرع قليلا من حجم بيانات المدخلة
July 2008 - September 2010
IBM Watson Center
- PostDoc Position
- Project title: OpenFOAM on BG/P
July 2005 - July 2008
- PhD Student
- Selected Publication: M.A. Abdou, S.A. Aseeri, Fourier integral transform and contact problem, Proc. The Second Conference On Mathematical Sciences, Zarqa, Jordan (2008)
The fast Fourier transform (FFT) has applications in almost every frequency related study, for example, in image and signal processing, and radio astronomy. It is also used as a Poisson operator inversion kernel in partial differential equations in fluid flows, in density functional theory, many‐body theory, and others. The three‐dimensional FFT ha...
The fast Fourier transform (FFT) has applications in almost every frequency related studies, e.g. in image and signal processing, and radio astronomy. It is also used to solve partial differential equations used in fluid flows, density functional theory, many-body theory, and others. Three-dimensional \(N^3\) FFT has large time complexity (O( N^3 l...
To determine the best method for solving a numerical problem modeled by a partial differential equation, one should consider the discretization of the problem, the computational hardware used and the implementation of the software solution. In solving a scientific computing problem, the level of accuracy can also be important, with some numerical m...
An overview of concerns observed in allowing for reproducibility in parallel applications that heavily depend on the three dimensional distributed memory fast Fourier transform are summarized. Suggestions for reproducibility categories for benchmark results are given.
The cubic Klein-Gordon equation is a simple but non-trivial partial differential equation whose numerical solution has the main building blocks required for the solution of many other partial differential equations. In this study, the library 2DECOMP&FFT is used in a Fourier spectral scheme to solve the Klein-Gordon equation and strong scaling of t...
In this paper, we consider a general conformal mapping function with complex constant coefficients, to solve the elasticity problems for an infinite plate weakened by a curvilinear hole. Conformal was used outside and inside of a unit circle in the presence of an initial heat flowing perpendicular to the plate. The use of the complex variable metho...
We used a rational mapping function with complex constants to derive exact and close expressions of Goursat functions for the first and second fundamental problems (plane elasticity problems) of an infinite plate weakened by a hole having arbitrary shape. Notable, the area outside the hole is conformally mapped outside a unit circle by means of the...
Here, we used a rational mapping function with complex constants in order to study the effect of complex constants. Also, a complex variable method have been applied to deduce exact expressions for Gaursat functions for the first and second fundamental problems of an infinite plate weakened by a hole having arbitrary shape. The edge of the hole is...
Complex variable method (Cauchy integral method) has been applied to derive exact and closed expressions of Goursat functions for the first and second fundamental problems for an infinite plate weakened by a curvilinear hole. The area outside the hole with the hole itself is con- formally mapped on the right half-plane by the use of a rational mapp...
There is need for computers which can solve problems that are larger than currently feasible, solve problems in less real time and solve problems using fewer resources. The fast Fourier transform has been named as one of the key algorithms of the 20th century. It is used in signal processing and in the accurate solution of partial differential equations. Current algorithmic implementations of the fast Fourier transform (and similar algorithms) require very many long range inter processor communications, which are a parallelization bottleneck. The scientific and engineering community still heavily uses the Fourier transform. In some cases, this can be replaced by fast multipole, multigrid and similar methods, which have lower communication complexity - though the effectiveness of these alternative methods for all problems for which the fast Fourier transform is being used is unclear. It seems that the fast Fourier transform will still be needed on exascale computers, though may not be an exascale algorithm. Over the upcoming year, viewpoints from developers and users of the fast Fourier transform and similar algorithms will be obtained to determine a consensus on the appropriate future direction for algorithmic and high performance computer hardware development that would allow for solution of problems where the fast Fourier transform is a key algorithmic component. Curated material from these discussions will be kept at http://www.fft.report, where additional contributions are welcome. We hope to have a closing meeting by mid 2019 followed by a journal special issue summarizing this outcome of all these discussions..