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Parallel Numerical Solution of Partial Differential Equations

Thesis Info

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Author

Muhammad Naveed Akhtar

Program

PhD

Institute

Pakistan Institute of Engineering and Applied Sciences

City

Islamabad

Province

Islamabad.

Country

Pakistan

Thesis Completing Year

2018

Thesis Completion Status

Completed

Subject

Computer Science

Language

English

Link

http://prr.hec.gov.pk/jspui/bitstream/123456789/10029/1/Muhammad_Naveed_Akhtar_Parallel_Computing_HSR_2018_PIEAS_01.10.2018.pdf

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676727807183

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Simulation of scientific problems is an important aspect of natural and engineering sciences. Simulations demanding higher accuracy or involving larger data sets require higher computing power. Complex mathematical models involving partial differential equations (PDEs) from computational fluid dynamics (CFD) are some examples of these simulations. The conventional serial computers are not able to meet the increasing demand of computation power for such applications and the only rescue is parallel or high-performance computing. This study presents research regarding parallel numerical solution of PDEs. Message Passing Interface (MPI) clusters and Graphic Processor Units (GPUs) being the leading platforms for parallel computing were used for simulation of results. The research begins with the unified analysis of the existing parallel iterative algorithms using MPI. A set of diverse PDEs was solved using the MPI cluster. After getting an insight of iterative methods for MPI platform, the parallel system with shared memory architecture was experimented. The most advent platform in this regard is GPUs having thousands of concurrent running cores along with many Giga bytes (GBs) of memory. 3D Laplace equation was solved using twelve different kernels to exploit the memory hierarchy of GPU and an efficient technique involving surfacing pointer’s capability of GPU was materialized. The GPU kernel exhibiting said features gained a speedup of 70 as compared to serial version of same program running on Intel core i5 processor. The derived technique was further extended to simulate the compressible, high-speed flows modeled by Navier Stokes equations using GPU. Four different structured geometries were modeled; the governing equations were solved using modified RK4 method and TVD scheme was used for shockwave capturing. The derived technique was also used to simulate the flow in micro channel using Lattice Boltzmann Method. The GPU results show a speedup of 23 and 77 as compared with serial variants of codes running on conventional core i5®CPU for both cases respectively. It is evident from obtained results that the performance of CFD and other compute intensive application can be enhanced many folds by using the devised technique involving surface pointers in GPU computation.
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لائبریری کی اہمیّت

لائبریری کی اہمیّت
ہم نشینی اگر کتاب سے ہو
اس سے بہتر کوئی رفیق نہیں
لائبریری سے مراد کتب خانہ ہے۔ لائبریری کی اہمیت سے مراداس چیز کی اہمیت نہیں کہ اس کی بلڈنگ کا خام مال بہت اچھا ہے، اس کے گردونواح اور مضافات کے باسی بہت اچھے ہیں۔ اس کے افتتاح کرنے والے کا کردار بہت اچھا ہے، اس کو بنانے والے کا کاروبار بہت اچھا ہے، اس حسین وجمیل بلڈنگ کو تعمیر کرنے والا معمار بہت اچھا ہے۔ لائبریری کی اہمیت سے مراد اس کے اندر جو کتب ہیں ان کا مطالعہ کتنی اہمیت کا حامل ہے، اس کے مطالعہ سے نوجوان کو کتنا فائدہ پہنچتا ہے، اس کے مطالعہ سے بوڑھے قاری کو کیا فائدہ پہنچتا ہے۔ اس کا مطالعہ معاشرے پر کیا اثرات مرتّب کرتا ہے۔
لائبریری کا وجود خواہ وہ سکول لائبریری ہو، خواہ وہ پبلک لائبریری ہو ،خواہ وہ ذاتی لائبریری ہو ملک و قوم کی تعمیر و ترقی میں انتہائی ضروری ہے۔ اساتذہ اور طلباء کے لیے کتب خانہ کی کتابوں کا مطالعہ انتہائی ناگزیر ہے، اسا تذہ کونئی تحقیقات سے بہرہ ور ہونے کا موقع میسر آتا ہے اور طلباء بھی اپنی نصابی اور غیر نصابی معلومات میں اضافہ کرتے ہیں۔ چنانچہ ہرتعلیمی ادارے میں معیاری لائبریری کا وجودضروری ہے۔ اس کے بغیر وہ ادارہ ایسا ہے جیسانخلستان چشمے کے بغیر یا ایک گھر پانی کے بغیر ،لائبریری گویا ایک چشمہ ہے جس کے آب زلال سے تشنگانِ علم و دانش اپنی پیاس بجھاتے ہیں۔
تاریخ کی ورق گردانی کریں تو یہ بات روزِ روشن کی طرح عیاں ہوتی ہے کہ مسلمانوں کو کتب بینی و مطالعہ میں ہمیشہ ایک امتیازی مقام حاصل رہا ہے۔ اسلام کے زمانۂ عروج میں مسلمان اُمراء میں لائبریری کا اہم مقابلہ ہوتا تھا۔ جس شخص کے پاس جتنا بڑا کتب خانہ...

HUBUNGAN ANTARA EFIKASI DIRI DAN PERAN GURU DENGAN BELAJAR BERDASAR REGULASI DIRI PADA AKSELERAN

This research is a quantitative approach with the aim at knowing: (1). The relationship between self-efficacy and the role of the teacher by learning based on self-regulation. (2). The contribution given by self-efficacy and the role of teachers in self-regulation based learning. (3). Levels of self-efficacy and the role of teachers in learning based on self-regulation. The subject of this study was acceleration in one of the Public High Schools in Surakarta as many as 115 people. This study is a principled study on population studies. Based on the results and analysis using multiple regression it is known that the correlation coefficient R = 0.375 (p = 0.000: p <0.05), which means that there is a significant relationship between self-efficacy and the role of teachers with self-regulation. The total contribution given by the two independent variables in this study amounted to 14.1%, and for both categorizations the independent variables namely self-efficacy and the role of the teacher were at a high level, and the dependent variable of learning based on self-regulation was at a very high level. Key word: Self-Regulated Learning, Self-Efficacy, The Role of Teachers

Prevalence of and Factors Associated With Vitamin D Deficiency Among Afghan Adolescents Diagnosed at a Tertiary Healthcare Facility in Kabul, Afghanistan

Background: Vitamin D, also known as the sunshine vitamin, is formed in the skin from exposure to sunlight, and is absorbed from foods as well. It is important for calcium absorption and bone growth. Vitamin D status is linked to the pathogenesis of skeletal and non-skeletal disorders. Vitamin D deficiency is relatively prevalent all over the world. In studies conducted in other countries, adolescents are thought to have increased risk of vitamin D deficiency. Still, data is lacking about the prevalence of vitamin D deficiency among healthy Afghan adolescents. Objective: The aim of this study was to determine the prevalence of and to identify factors associated with vitamin D deficiency and severe vitamin D deficiency among Afghan adolescents (10-18 years of age) diagnosed at French Medical Institute for Mothers and Children (FMIC), Kabul. Material and Methods: An analytical cross-sectional study design was conducted from Jun to Sep 2016. Blood samples were obtained, serum 25OHD levels were measured, and the patients were divided into five diagnostic categories according to their serum 25OHD concentrations. 1) Sufficiency ≥30-100 ng/ml; 2) Insufficiency ≥20-30 ng/ml; 3) Deficiency <20 ng>/ml; 4) Severe deficiency <10 ng>/ml; 5) Intoxication >150 ng/ml. Collection of samples were made at Clinical Laboratory of FMIC and serum 25OHD analyses were carried out in the Biochemistry section. Results: A total of 308 adolescents were part of the sample for the final analysis. Of all, 202 (65.6%) were females and 106 (34.5%) were males. Out of total, 238 (77.3%) had either insufficiency, deficiency or severe deficiency of vitamin D. Among those, a large number of the participantss i.e., 107 (34.7%) had severe vitamin D deficiency, 81 (26.3%) had vitamin D deficiency, 50 (16.2%) had vitamin D insufficiency, and only 70 (22.7%) had vitamin D sufficiency. There were two cases of vitamin D intoxication, who were excluded from the study. Gender, sun-exposure, usage of sun protector, calcium+vitamin D supplement intake, Vitamin D rich foods intake, regular milk intake, the type of living in yards or apartments, skin colour of participants, and BMI were found as significant factors associated with vitamin D level Conclusion: There was a high prevalence of vitamin D deficiency among adolescents who visited a tertiary healthcare facility in Kabul. Low serum vitamin D concentration is prevalent among general Afghan population. Screening and ongoing investigation for vitamin D deficiency should be considered for all adolescents in the country. Based on our results, the