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مروری بر روشهای محاسبه انتگرالهای درون دامنه در روش المان‌های مرزی

نوع مقاله : مقاله مروری

نویسندگان

1 دانشگاه دانشگاه صنعتی اصفهان

2 دانشگاه صنعتی اصفهان

چکیده

این مقاله به مروری بر انواع روش‌های حل انتگرال‌های داخل دامنه در روش المان‌های مرزی می‌پردازد. ظهور انتگرال‌های درون دامنه در فرمول‌بندی روش اجزای مرزی، عمدتاً از جمله اینرسی در مسائل دینامیکی، نیروهای بدنه در مسائل استاتیکی و یا اثرات ناهمگنی ماده نشأت می‌گیرد. در حل مسائل با استفاده از روش‌های المان‌های مرزی رویکردهای متعددی برای محاسبه انتگرال‌های مرزی و درون دامنه وجود دارد. انتخاب نوع روش انتگرال‌گیری تاثیر بسیار مهمی بر سرعت و دقت حل مسئله دارد. در این تحقیق، مروری جامعی از روش‌های محاسبه انتگرال‌های درون دامنه با دو نگرش مبتنی بر شبکه‌بندی دامنه و گسسته‌سازی منحصر به مرز، ارائه خواهد شد. با توجه به محبوبیت رویکردهای بدون نیاز به شبکه‌بندی دامنه، در این بررسی تمرکز بیشتری به ارائه فرمول‌بندی چنین روش‌هایی اختصاص یافته و دو روش متداول تقابل دوگانه و انتگرال‌گیری شعاعی به عنوان شیوه کارآمدتر و سریع‌تر از میان این روش‌ها شرح داده می‌شوند. در پایان نیز جزییات روش انتگرال‌گیری شعاعی اصلاح شده برای محاسبه انتگرال‌های درون دامنه‌های غیر محدب بیان خواهد شد.

کلیدواژه‌ها

عنوان مقاله [English]

A Review on Techniques of Domain Integrals Computation in Boundary Elements Method

نویسندگان [English]

  • Leila Najarzadeh 1
  • Bashir Movahedian Attar 2
  • Mojtaba Azhari 2

چکیده [English]

In this article, a review of the evaluation methods of the domain integrals in the boundary element method will be presented. The emergence of domain integrals in the formulation of the boundary element method mainly originates from the inertia term in dynamic problems, body forces in static problems or the effects of material heterogeneity. There are several approaches to calculate boundary and domain integrals in boundary element methods. Choosing the type of integration method has a prominent effect on the accuracy of the numerical solution. In this research, a comprehensive review on the techniques of domain integrals computation will be presented based on two approaches, i.e. domain splitting, and converting the domain integrals to boundary ones. The review focuses primarily on the formulation of approaches without requiring domain splitting, because of their popularity. Among them, the dual reciprocity method and the radial integration method have been described as the most efficient. At the end, the details of the modified radial integration method for calculating the integrals within non-convex domains will be stated.  

کلیدواژه‌ها [English]

  • Boundary elements method
  • Domain integrals
  • Dual reciprocity method
  • Modified radial integration method
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