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Electromagnetic Scattering Simulation Based on SPH Method Using GPU Parallel Processing
Barkhordari, Alireza | 2014
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- Type of Document: M.Sc. Thesis
- Language: Farsi
- Document No: 45589 (05)
- University: Sharif University of Technology
- Department: Electrical Engineering
- Advisor(s): Shishegar, AmirAhmad
- Abstract:
- In this thesis, we propose and discuss efficient GPU implementation using CUDA for simulating electromagnetic scattering. We use SPH as a meshless particle method to electromagnetic transient simulation in time domain. Smoothed particle hydrodynamics (SPH) has been recently reformulated by the authors, and implemented in the so-called smoothed particle electromagnetics (SPEM) method. In SPEM two set of electric and magnetic staggered particles have to be generated. These particles are the points in which the field components are computed at each time step by using the information belonging to the neighboring ones.
On the other hand, CUDA™ is a general purpose parallel computing platform and programming model that leverages the parallel compute engine in NVIDIA GPUs to solve many complex computational problems in a more efficient way than on a CPU.
We used these tools and make an efficient program that can calculate electromagnetic fields about 10 times faster than serial one.
- Keywords:
- Parallel Processing ; Electromagnetic Wave Scattering ; Smoothed Particle Hydrodynamics (SPH) ; Graphic Processing
- محتواي کتاب
- view
- فصل 1: معرفی
- فصل 2: آشنايي با روش SPH و کاربرد آن در شبيهسازي الکترومغناطيسي
- 2-1- روند کلي حل به کمک روشهاي عددي
- 2-2- روشهاي مبتني بر شبکه
- 2-3- روشهاي بدون شبکه
- 2-4- مقدماتي درباره استفاده از SPH در الکترومغناطيس
- (2-9) ,-ℎ.,,.=,Ω--(−,-′.,ℎ(,))(,-′.,),.′.
- (2-10) ,-ℎ.,,.≅,=1--(−,-.,ℎ(,))(,-.,)∆,-..
- (2-11) ,−,-′.,ℎ.=,-.,−,-2..
- (2-12) =,,1-ℎ,..., =,,−,-′..-ℎ.
- (2-13) ,-.=,,,1-ℎ,...-2.,−,,,,−,-′..-ℎ..-2..,−,2-,ℎ-2...×,,−,-′. ; =-−,-′. ; =..
- 2-4-2- چگونگي عملکرد اپراتورهاي ديفرانسيلي
- (2-15) ,∇.,..=,Ω--,,∇-′..,,-′...(−,-′.,ℎ),-′..
- (2-16) ,∇.,..=,Ω--,∇-′..,,,-′..,−,-′.,ℎ..,-′..−,Ω--,,-′...,∇-′.,−,-′.,ℎ.,-′..
- (2-17) ,∇.,..=,--,,,-′..,−,-′.,ℎ..,..,-′..−,Ω--,,-′...,∇-′.,−,-′.,ℎ.,-′..
- شکل (2-5) دامنه پشتيباني تابع هموارکننده و دامنه مسئله بدون همپوشاني [1]
- شکل (2-6) دامنه پشتيباني تابع هموارکننده و دامنه مسئله با وجود همپوشاني [1]
- 2-5- اعمال روش SPH بر معادلات ماکسول (SPEM )
- (2-19) ∇×=−,-.
- (2-20) ∇×=,-.+
- (2-21) ,,,,-.-.−,,-.-.=−,,-.-.-,,-.-.−,,-.-.=−,,-.-.-,,-.-.−,,-.-.=−,,-.-...
- (2-22) ,,,,-.-.−,,-.-.=,,-.-.+,-.-,,-.-.−,,-.-.=,,-.-.+,-.-,,-.-.−,,-.-.=,,-.-.+,-...
- 2-5-2- حالت يک بعدي
- (2-23) ,,,,-.-.=−,,-.-.-−,,-.-.=,,-.-.+,-...
- (2-24) ,,−,,-.-.=−,,-.-.-,,-.-.=,,-.-.+,-...
- (2-25) ,,-.,,-..-.=,1-.,=1-,-.-,-.,,-..,(,-.−,-.,ℎ)-,-..,-..
- (2-26) ,,-.,,-..-.=,1-.,=1-,-.-,-.,,-..,(,-.−,-.,ℎ)-,-..,-..
- (2-27) ,--+1.,,--..=,--.,,--..+,∆-.,=1-,-.-,--+,1-2..,,--..,(,--.−,--.,ℎ)-,--..,-..
- (2-28) ,--+,1-2..,,--..=,--−,1-2..,,--..+,∆-.,=1-,-.-,--.,,--..,(,--.−,--.,ℎ)-,--..,-..
- 2-5-3- حالت دو بعدي
- (2-29) ,,,,-.-.=−,,-.-.-−,,-.-.=−,,-.-.-,,-.-.−,,-.-.=−,,-.-...
- (2-30) ,,,,-.-.=,,-.-.+,-.-−,,-.-.=,,-.-.+,-.-,,-.-.−,,-.-.=,,-.-.+,-...
- (2-31) ,,,,-.-.=−,,-.-.-−,,-.-.=−,,-.-.-,,-.-.−,,-.-.=,,-.-.+,-...
- (2-32) ,,,,-.-.=,,-.-.+,-.-−,,-.-.=,,-.-.+,-.-,,-.-.−,,-.-.=−,,-.-...
- (2-33) ,,-.,,-..-.=−,1-.,=1-,-.-,-.,,-..,(,-.−,-.,ℎ)-,-..,-..
- (2-34) ,,-.,,-..-.=,1-.,=1-,-.-,-.,,-..,(,-.−,-.,ℎ)-,-..,-..
- (2-35) ,,-.,,-..-.=,1-.,=1-,-.-,,-.,,-..,(,-.−,-.,ℎ)-,-..−,-.,,-..,(,-.−,-.,ℎ)-,-...,-..
- (2-36) ,,-.,,-..-.=−,1-.,=1-,-.-,-.,,-..,(,-.−,-.,ℎ)-,-..,-..
- (2-37) ,,-.,,-..-.=,1-.,=1-,-.-,-.,,-..,(,-.−,-.,ℎ)-,-..,-..
- (2-38) ,,-.,,-..-.=,1-.,=1-,-.-,,-.,,-..,(,-.−,-.,ℎ)-,-..−,-.,,-..,(,-.−,-.,ℎ)-,-...,-..
- (2-39) ,--+1.,,--..=,--.,,--..−,∆-.,=1-,-.-,--+,1-2..,,--..,(,--.−,--.,ℎ)-.,-..
- (2-40) ,--+1.,,--..=,--.,,--..+,∆-.,=1-,-.-,--+,1-2..,,--..,(,--.−,--.,ℎ)-.,-..
- (2-42) ,--+,1-2..,,--..=,--−,1-2..,,--..−,∆-.,=1-,-.-,--.,,--..,(,--.−,--.,ℎ)-.,-..
- (2-43) ,--+,1-2..,,--..=,--−,1-2..,,--..+,∆-.,=1-,-.-,--.,,--..,(,--.−,--.,ℎ)-.,-..
- 2-5-4- اعمال شرط مرزي PML بر روابط SPH در حالت دو بعدي
- (2-45) ,-.,,.×.=−,,-.-.−,,-.-.,-.
- (2-46) ,-.,,.×.=−,,-.-.−,,-.-.,-.
- (2-47) ,-.,,.×.=−,,-.-.−,,-.-.,-.
- (2-48) ,-.,,.×.=,,-.-.+,-.,-.
- (2-49) ,-.,,.×.=,,-.-.+,-.,-.
- (2-50) ,-.,,.×.=,,-.-.+,-.,-.
- (2-51) ,-.+,-.+,-.=
- (2-52) ,-.+,-.+,-.=
- (2-53) ,-.,-.=,,-.-.+,,-.-.,-.
- (2-54) ,-.,-.=−,,-.-.−,,-.-.,-.
- (2-55) ,-.,-.=,,-,.-.+,-.,-,.+,-.
- (2-56) ,-.,-.=−,,-,.-.−,-.,-,.
- 2-5-5- حالت سه بعدي
- (2-61) ,,-.-.−,,-.-.=−,,-.-.
- (2-66) ,∂,E-.-∂t.,,--..=,1-.,=1--,,-.,,--..,--.−,-.,,--..,--..∆,-.+,,-.,,--..-..
- (2-67) ,∂,E-.-∂t.,,--..=,1-.,=1--,,-.,,--..,--.−,-.,,--..,--..∆,-.+,,-.,,--..-..
- (2-68) ,∂,E-.-∂t.,,--..=,1-.,=1--,,-.,,--..,--.−,-.,,--..,--..∆,-.+,,-.,,--..-..
- (2-69) ,∂,H-.-∂t.,,--..=−,1-.,=1--,,-.,,--..,--.−,-.,,--..,--..∆,-..
- (2-70) ,∂,H-.-∂t.,,--..=−,1-.,=1--,,-.,,--..,--.−,-.,,--..,--..∆,-..
- (2-71) ,∂,H-.-∂t.,,--..=−,1-.,=1--,,-.,,--..,--.−,-.,,--..,--..∆,-..
- (2-72) ,--.=,-.(,--.−,--.,,ℎ--.)
- (2-73) ,--.=,-.(,--.−,--.,,ℎ--.)
- (2-76) ,H--+1.,,--..=,H--.,,--..+,∆-.,=1--,,--+,1-2..,,--..,--.−,--+,1-2..,,--..,--..∆,-..
- (2-80) ,H--+1.,,--..=,H--.,,--..−,∆-.,=1--,,--+,1-2..,,--..,--.−,--+,1-2..,,--..,--..∆,-..
- (2-81) ,H--+1.,,--..=,H--.,,--..−,∆-.,=1--,,--+,1-2..,,--..,--.−,--+,1-2..,,--..,--..∆,-..
- (2-82) ,H--+1.,,--..=,H--.,,--..−,∆-.,=1--,,--+,1-2..,,--..,--.−,--+,1-2..,,--..,--..∆,-..
- (2-83) ∆≪,,,ℎ-.,,-.,-..-,-0...
- 2-5-6- اعمال شرط مرزي PML بر روابط SPH در حالت سه بعدي
- (2-84) ,-.,,.×.=−,,-.-.−,,-.-.,-.
- (2-85) ,-.,,.×.=−,,-.-.−,,-.-.,-.
- (2-86) ,-.,,.×.=−,,-.-.−,,-.-.,-.
- (2-87) ,-.,,.×.=,,-.-.+,-.,-.
- (2-88) ,-.,,.×.=,,-.-.+,-.,-.
- (2-89) ,-.,,.×.=,,-.-.+,-.,-.
- (2-90) ,-.+,-.+,-.=
- (2-91) ,-.+,-.+,-.=
- (2-92) ,-.,-.=−,,-,.-.−,,-.-.,-,.
- (2-93) ,-.,-.=,,-,.-.+,,-.-.,-,.
- (2-94) ,-.,-.=,,-,.-.+,,-.-.,-,.
- (2-95) ,-.,-.=−,,-,.-.−,,-.-.,-,.
- (2-96) ,-.,-.=−,,-,.-.−,,-.-.,-,.
- (2-97) ,-.,-.=,,-,.-.+,,-.-.,-,.
- (2-98) ,-.,-.=,,-,.-.+,-.,-,.
- (2-99) ,-.,-.=−,,-,.-.−,-.,-,.
- (2-100) ,-.,-.=−,,-,.-.−,-.,-,.
- (2-101) ,-.,-.=,,-,.-.+,-.,-,.
- (2-102) ,-.,-.=,,-,.-.+,-.,-,.
- (2-103) ,-.,-.=−,,-,.-.−,-.,-,.
- (2-104) ,-.,-.=−,,H-,-+1.,,--..−,H-,-.,,--..-∆.−,,-.-.,,H-,-+1.,,--..+,H-,-.,,--..-2.
- (2-105) ,H-,-+1.,,--..=,1-,,-∆.+,,-.-2...,,,-∆.−,,-.-2..,H-,-.,,--..−,=1--,-.,,--..,--.∆,-...
- (2-106) ,H-,-+1.,,--..=,1-,−,-∆.−,,-.-2...,,−,-∆.+,,-.-2..,H-,-.,,--..−,=1--,-.,,--..,--.∆,-...
- (2-107) ,H-,-+1.,,--..=,1-,−,-∆.−,,-.-2...,,−,-∆.+,,-.-2..,H-,-.,,--..−,=1--,-.,,--..,--.∆,-...
- (2-108) ,H-,-+1.,,--..=,1-,,-∆.+,,-.-2...,,,-∆.−,,-.-2..,H-,-.,,--..−,=1--,-.,,--..,--.∆,-...
- (2-109) ,H-,-+1.,,--..=,1-,,-∆.+,,-.-2...,,,-∆.−,,-.-2..,H-,-.,,--..−,=1--,-.,,--..,--.∆,-...
- (2-110) ,H-,-+1.,,--..=,1-,−,-∆.−,,-.-2...,,−,-∆.+,,-.-2..,H-,-.,,--..−,=1--,-.,,--..,--.∆,-...
- (2-111) ,E-,-+,1-2..,,--..=,1-,−,-∆.−,,-.-2...,,−,-∆.+,,-.-2..,E-,-−,1-2..,,--..−,=1--,-.,,--..,--.∆,-...
- (2-112) ,E-,-+,1-2..,,--..=,1-,,-∆.+,,-.-2...,,,-∆.−,,-.-2..,E-,-−,1-2..,,--..−,=1--,-.,,--..,--.∆,-...
- (2-113) ,E-,-+,1-2..,,--..=,1-,,-∆.+,,-.-2...,,,-∆.−,,-.-2..,E-,-−,1-2..,,--..−,=1--,-.,,--..,--.∆,-...
- (2-114) ,E-,-+,1-2..,,--..=,1-,−,-∆.−,,-.-2...,,−,-∆.+,,-.-2..,E-,-−,1-2..,,--..−,=1--,-.,,--..,--.∆,-...
- (2-115) ,E-,-+,1-2..,,--..=,1-,−,-∆.−,,-.-2...,,−,-∆.+,,-.-2..,E-,-−,1-2..,,--..−,=1--,-.,,--..,--.∆,-...
- (2-116) ,E-,-+,1-2..,,--..=,1-,,-∆.+,,-.-2...,,,-∆.−,,-.-2..,E-,-−,1-2..,,--..−,=1--,-.,,--..,--.∆,-...
- (2-125) ,-,.,,.=,−1-,,-∆.+,,-.-2...,-.(,--.−,--.,,ℎ--.)∆,-.
- (2-126) ,-,.,,.=,1-,,-∆.+,,-.-2...,-.(,--.−,--.,,ℎ--.)∆,-.
- (2-127) ,-,.,,.=,1-,,-∆.+,,-.-2...,-.(,--.−,--.,,ℎ--.)∆,-.
- (2-128) ,-,.,,.=,−1-,,-∆.+,,-.-2...,-.(,--.−,--.,,ℎ--.)∆,-.
- (2-129) ,-.=,-,.+,-,.
- (2-130) ,-.=,-,.+,-,.
- 2-6- تابع هموار کننده و مشتقاتش
- 2-7- مروري بر مقالات
- 2-8- استفاده از ADI-FDTD
- (2-133) ∇×=−,-.
- (2-134) ∇×=,-.+
- (2-135) ,,-.-.=,1-.,,,-.-.−,,-.-..
- (2-136) ,,-.-.=,1-.,,,-.-.−,,-.-.−,-..
- (2-137) ,2-∆.,,--−,1-2..−,--−1..=,1-.,,,--−,1-2..-.−,,--−1.-.−,-..
- (2-138) ,2-∆.,,--−,1-2..−,--−1..=,1-.,,,--−,1-2..-.−,,--−1.-..
- (2-139) ,2-∆.,,--.−,--−,1-2...=,1-.,,,--−,1-2..-.−,,--.-.−,-..
- (2-140) ,2-∆.,,--.−,--−,1-2...=,1-.,,,--−,1-2..-.−,,--.-..
- (2-141) ,--−,1-2..=,--−1.+,∆-2.,,,--−,1-2..-.−,,--−1.-.−,-..
- (2-142) ,--−,1-2..=,--−1.+,∆-2.,,,--−,1-2..-.−,,--−1.-..
- (2-143) ,--.=,--−,1-2..+,∆-2.,,,--−,1-2..-.−,,--.-.−,-..
- (2-144) ,--.=,--−,1-2..+,∆-2.,,,--−,1-2..-.−,,--.-..
- (2-145) ,--−,1-2..=,--−1.+,∆-2.,,,--−1.-.+,∆-2.,-.,,,--−,1-2..-.−,,--−1.-..−,,--−1.-.−,-..
- (2-146) ,--.=,--−,1-2..+,∆-2.,,,--−,1-2..-.+,∆-2.,-.,,,--.-.−,,--−,1-2..-..−,,--−,1-2..-.−,-..
- (2-147) ,--−,1-2..=,--.−,∆-2.,,,--−,1-2..-.−,,--.-..
- (2-148) ,--.=,--−,1-2..+,∆-2.,,-.,,--.+,∆-2.,,,--−,1-2..-.−,,--.-...−,,--.-.−,-..
- (2-149) ,--+,1-2..=,--.+,∆-2.,,,--.-.+,∆-2.,-.,,,--+,1-2..-.−,,--.-..−,,--.-.−,-..
- (2-150) ,--+,1-2..−,1-.,,,∆-2..-2.,,-2.,--+,1-2..-,-2..=,--−,1-2..−,1-.,,,∆-2..-2.,,-2.,--−,1-2..-,-2..+∆,,,--.-.−,,--.-.−,-..
- (2-151) ,--+1.=,--+,1-2..+,∆-2.,,,--+,1-2..-.−,,--+1.-..
- (2-152) ,--+1.=,--+,1-2..+,∆-2.,,,--+,1-2..-.−,-.,,--+,1-2..+,∆-2.,,,--+,1-2..-.−,,--+1.-....
- (2-153) ,--+,1-2..=,--.+,∆-2.,,,--+,1-2..-.−,,--.-..
- (2-154) ,--+1.=,--.+,∆-2.,,,--+,1-2..-.−,-.,,--+,1-2..+,∆-2.,,,--+,1-2..-.−,,--.-....
- (2-155) ,--+1.−,,,∆.-2.-4.,,-2.,--+1.-,-2..=,--.−,,,∆.-2.-4.,,-2.,--.-,-2..+,∆-.,,,--+,1-2..-.−,,--+,1-2..-..
- (2-158) ,--.,--+,1-2..=,--.,--−,1-2..+,--.,--.+,--.,--.
- (2-159) ,--.=,,,--.,,..-×.
- (2-160) ,--.,,.=,,−,,,∆-2..-2.,1-.,,-2.,-,-,.-,-2..∆,-. ;=-−,,,∆-2..-2.,1-.,,-2.,-,-,.-,-2..∆,-. ;≠ ..
- (2-161) ,--.=,,,--.,,..-×.
- (2-162) ,--.,,.=∆,,-,-,.-.∆,-.
- (2-163) ,--.=,,,--.,,..-×.
- (2-164) ,--.,,.=−∆,,-,-,.-.∆,-.
- (2-165) ,--.,--+1.=,--.,--.+,--.,--+,1-2..+,--.,--+,1-2..
- (2-166) ,--.=,,,--.,,..-×.
- (2-167) ,--.,,.=,,−,,,∆-2..-2.,1-.,,-2.,-,-,.-,-2..∆,-. ;=-−,,,∆-2..-2.,1-.,,-2.,-,-,.-,-2..∆,-. ;≠ ..
- (2-168) ,--.=,,,--.,,..-×.
- (2-169) ,--.,,.=,∆-.,,-,-,.-.∆,-.
- (2-170) ,--.=,,,--.,,..-×.
- (2-171) ,--.,,.=−,∆-.,,-,-,.-.∆,-.
- 2-9- سازگاري در روش SPH
- 2-9-1- مفهوم سازگاري يک تقريب
- 2-9-2- ترميم سازگاري در SPEM
- (2-184) ,E--+,1-2..,,--..=,E--−,1-2..,,--..+,∆-.,,,--.-.,,--..−,,--.-.,,--..+,E--−,1-2..,,--...
- (2-185) ,E--+,1-2..,,--..=,E--−,1-2..,,--..+,∆-.,,,--.-.,,--..−,,--.-.,,--..+,E--−,1-2..,,--...
- (2-186) ,E--+,1-2..,,--..=,E--−,1-2..,,--..+,∆-.,,,--.-.,,--..−,,--.-.,,--..+,E--−,1-2..,,--...
- (2-187) ,H--+1.,,--..=,H--.,,--..−,∆-.,,,--+,1-2..-.,,--..−,,--+,1-2..-.,,--...
- (2-188) ,H--+1.,,--..=,H--.,,--..−,∆-.,,,--+,1-2..-.,,--..−,,--+,1-2..-.,,--...
- (2-189) ,H--+1.,,--..=,H--.,,--..−,∆-.,,,--+,1-2..-.,,--..−,,--+,1-2..-.,,--...
- فصل 3: آشنايي با پردازش موازي و CUDA
- 3-1- مقدمه
- 3-2- پردازش موازي
- 3-3- CUDA
- 3-4- آشنايي با برنامه نويسي CUDA
- 3-5- معماري پردازندهي گرافيکي
- 3-6- قابليت پردازش
- فصل 4: پيادهسازي و نتايج
- 4-1- معرفي پردازنده گرافيکي استفاده شده
- 4-2- يافتن نزديکترين گره ها در همسايگي
- 4-3- خط جريان بينهايت در فضاي آزاد
- 4-4- پراکندگي موج صفحهاي از استوانه هادي بينهايت
- 4-4-1- استفاده از روش ميدان کل/ميدان پراکنده شده
- 4-4-2- چگونگي استفاده از Shared memory
- 4-4-3- محدوديت هاي حافظه
- 4-4-4- استفاده از کرنل هاي جداگانه براي نواحي مختلف
- 4-4-5- نتايج
- شکل (4-15) مقايسه نتايج روشهاي FDTD و SPEM در نقطهي (-1.5,0)
- شکل (4-16) مقايسه نتايج روشهاي FDTD و SPEM در نقطهي (1.5,0)
- شکل (4-17) مقايسه نتايج روشهاي FDTD و SPEM در نقطهي (0,-1.5)
- شکل (4-18) مقايسه نتايج روشهاي FDTD و SPEM در نقطهي (0,1.5)
- شکل (4-19) نمايي از ميدان کل و ميدان پراکنده شده از استوانهي هادي. ميدان تابشي از سمت پايين به استوانه برخورد کرده است
- 4-5- پيشنهادات
- مراجع