A Novel Strategy for Eliminating the Boundary Layer Effect in the Regularized Integral Identity in PIES for 2D Potential Problem

IF 1.6 4区 工程技术 Q2 ENGINEERING, MULTIDISCIPLINARY
E. Zieniuk, K. Szerszen, A. Bołtuć
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引用次数: 0

Abstract

The paper presents a new strategy for improving the accuracy of solutions near the boundary in the integral identity associated with the parametric integral equation system (PIES) for two-dimensional (2D) potential problems. A significant reduction in accuracy in the zone close to the boundary, also known as the boundary layer effect, is directly associated with the nearly singular properties of kernels present in the integral identity. The paper shows that these singularities can be efficiently eliminated by regularizing the integral identity with the help of the so-called regularizing function with appropriate coefficients. The analyzed examples demonstrate a significant improvement in accuracy, where all integrals of the regularized integral identity are accurately calculated using low-order standard Gauss–Legendre quadrature. The proposed regularization algorithm is independent of the actual boundary shape, its representation and assumed boundary conditions.
一种消除二维势问题PIES正则积分恒等式中边界层效应的新策略
本文提出了一种新的策略来提高二维(2D)势问题的参数积分方程组(PIES)积分恒等式边界附近解的精度。在靠近边界的区域中,精度的显著降低,也称为边界层效应,与积分恒等式中存在的核的几乎奇异性质直接相关。本文证明,借助于具有适当系数的正则化函数,通过正则化积分恒等式,可以有效地消除这些奇异性。分析的例子证明了精度的显著提高,其中正则积分恒等式的所有积分都是使用低阶标准高斯-勒让德求积精确计算的。所提出的正则化算法与实际边界形状、其表示和假设的边界条件无关。
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来源期刊
International Journal of Computational Methods
International Journal of Computational Methods ENGINEERING, MULTIDISCIPLINARY-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS
CiteScore
3.30
自引率
17.60%
发文量
84
审稿时长
15 months
期刊介绍: The purpose of this journal is to provide a unique forum for the fast publication and rapid dissemination of original research results and innovative ideas on the state-of-the-art on computational methods. The methods should be innovative and of high scholarly, academic and practical value. The journal is devoted to all aspects of modern computational methods including mathematical formulations and theoretical investigations; interpolations and approximation techniques; error analysis techniques and algorithms; fast algorithms and real-time computation; multi-scale bridging algorithms; adaptive analysis techniques and algorithms; implementation, coding and parallelization issues; novel and practical applications. The articles can involve theory, algorithm, programming, coding, numerical simulation and/or novel application of computational techniques to problems in engineering, science, and other disciplines related to computations. Examples of fields covered by the journal are: Computational mechanics for solids and structures, Computational fluid dynamics, Computational heat transfer, Computational inverse problem, Computational mathematics, Computational meso/micro/nano mechanics, Computational biology, Computational penetration mechanics, Meshfree methods, Particle methods, Molecular and Quantum methods, Advanced Finite element methods, Advanced Finite difference methods, Advanced Finite volume methods, High-performance computing techniques.
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