Lambert probleminin modifiye Chebyshev-Picard yineleme yöntemini kullanarak paralel çözümü

Öz

Lambert problemi, yörünge belirlemede çoklu devir problemini çözmek için kullanılan klasik yöntemlerden biridir. Uzay araştırma programlarına ve uydu ağlarının kullanımına olan ilginin artmasıyla, ağ kontrol merkezine ağdaki her bir uydunun yörüngesine ilişkin bilgileri sağlayacak ve uyduların yönlendirme kararlarını iyileştirmesine yardımcı olacak doğru ve hızlı bir yöntemin sağlanması önemlidir. Lambert problemi, bu problemi yinelemeli olarak çözen yöntemlerden biridir ve bu yineleme önceki yıllarda Newton'un yineleme yöntemi kullanılarak yapılmaktaydı. Daha güncel araştırmalarda bu problemi çözmek için Chebyshev-Picard yineleme yöntemi kullanılması önerilmektedir. Önerilen metot çözüm süresinde iyileştirmeler sunmasına rağmen büyük problemlerde çözüm çok uzun süreler alabilmektedir. Bu çalışmada, Lambert problemini paralel programlama teknikleri kullanarak daha hızlı çözen yeni bir paralel algoritma önerilmiştir. Ayrıca algoritmanın paralel ölçeklenebilirliğini göstermek için 2 farklı paralel sistemde; paylaşımlı ve dağıtık bellek mimarilerinde deneyler yapılmıştır. Deneysel sonuçlar, paralel algoritmanın dağıtık bellek ve paylaşımlı bellek mimarilerinde sırasıyla 8.26 ve 3.94 kat daha hızlı çözüm süresine ulaştığını göstermektedir.

Anahtar Kelimeler

• Lambert problemi
• Yörünge belirleme
• Yüksek performanslı hesaplama
• Lambert problemi
• Modifiye Chebyshev-Picard yinelemesi
• Yörünge belirleme
• Paralel hesaplama

Parallel solution of Lambert’s problem using modified Chebyshev-Picard iteration method

Abstract

Lambert’s problem is one of the classical methods for solving the multiple revolution problem in orbit determination. With the increasing interest in space exploration programs and using satellite networks, it is important to provide an accurate and rapid method that will provide the network control center with information regarding the orbit of each satellite in the network and help the satellites improve routing decisions in onboard processing satellites. Lambert’s problem is one of the methods that solve the problem iteratively and this iteration was originally done using Newton’s iteration method. In recent studies, it is recommended to use the Chebyshev-Picard iteration method to solve this problem. Since the aim here is to provide a method that solves the problem rapidly, the Chebyshev-Picard iteration method serves our objective since it is highly parallelizable. In this work, we have developed a parallel algorithm that solves Lambert’s problem in a parallel environment. We have conducted experiments to demonstrate the parallel scalability of the algorithm on both shared and distributed memory architectures. The experimental results show that the parallel algorithm achieves 8.26- and 3.94-times faster execution time on distributed memory and shared memory architectures, respectively.

Keywords

• Lambert’s problem
• Orbit determination
• Parallel computing.
• High performance computing
• Lambert’s problem
• Modified Chebyshev-Picard iteration
• Orbit determination
• Parallel computing.

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