PARALLEL MESHLESS RADIAL BASIS FUNCTION COLLOCATION METHOD FOR NEUTRON DIFFUSION PROBLEMS

Öz

The meshless global radial basis function (RBF) collocation method is widely used to model physical phenomena in science and engineering. The method produces highly accurate solutions with an exponential convergence rate. However, due to the global approximation structure of the method, dense node distributions lead to long computation times and hinder the applicability of the technique. In order to overcome this issue, this study proposes a parallel meshless global RBF collocation algorithm. The algorithm is applied to 2-D neutron diffusion problems. The multiquadric is used as the RBF. The algorithm is developed with Mathematica and eight virtual processors are used in calculations on a multicore computer with four physical cores. The method provides accurate numerical results in a stable manner. Parallel speedup increases with the number of processors up to five and seven processors for external and fission source problems, respectively. The speedup values are limited by the constrained resource sharing of the multicore computer’s memory. On the other hand, significant time savings are achieved with parallel computation. For the four-group fission source problem, when 4316 interpolation nodes are employed, the utilization of seven processors instead of sequential computation decreases the computation time of the meshless approach by 716 s.

Anahtar Kelimeler

• Parallel
• Meshless
• Radial Basis Function
• Collocation
• Neutron diffusion

Nötron difüzyon problemleri için paralel ağsız radyal baz fonksiyonu kollokasyon yöntemi

Öz

Ağsız global radyal baz fonksiyonu (RBF) kollokasyon yöntemi bilim ve mühendislikte karşılaşılan fiziksel olayların modellenmesinde yaygın bir şekilde kullanılmaktadır. Yöntem, üstel bir yakınsama hızı ile yüksek doğruluğa sahip çözümler üretir. Fakat, yöntemin global yaklaşım yapısı nedeniyle, çok sayıda ayrıklaştırma noktası kullanılması hesaplama sürelerini uzatmakta ve yöntemin uygulanabilirliğini kısıtlamaktadır. Söz konusu sorunun üstesinden gelebilmek için bu çalışmada bir paralel ağsız global RBF kollokasyon algoritması önerilmiştir. Algoritma iki boyutlu nötron difüzyon problemlerine uygulanmıştır. Multikuadrik fonksiyonu RBF olarak kullanılmıştır. Algoritma, Mathematica yazılımı ile geliştirilmiş ve hesaplamalar dört fiziksel çekirdeğe sahip çok çekirdekli bir bilgisayar ile sekiz sanal işlemci ile gerçekleştirilmiştir. Yöntem, doğru sayısal sonuçları kararlı bir şekilde sunmuştur. Paralel hızlanma işlemci sayısıyla, dış ve fisyon kaynağı problemleri için, sırasıyla beş ve yedi işlemciye kadar artmaktadır. Hızlanma değerleri çok çekirdekli bilgisayar belleğinin sınırlı kaynak paylaşımı nedeniyle kısıtlanmıştır. Diğer taraftan, paralel hesaplama ile önemli zaman kazanımları elde edilmiştir. Dört-grup fisyon kaynağı problemi için, 4316 interpolasyon noktası kullanılması durumunda, seri hesaplama yerine yedi işlemci kullanılması ağsız yöntemin hesaplama süresini 716 s kısaltmıştır.

Anahtar Kelimeler

• Paralel
• Ağsız
• Radyal baz fonksiyonu
• Kollokasyon
• Nötron difüzyonu

Kaynakça

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