An algebraic formulation of the simplex linear method for multiple integrals over the d-dimensional domain |
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| Authors: | S. Kaprzyk |
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| Affiliation: | 1. National Renewable Energy Laboratory, Golden, CO 80401, USA;2. Department of Physics, Kyung Hee University, Seoul 130-701, Republic of Korea;3. Department of Physics and Astronomy, University of Toledo, Toledo, OH 43606, USA;4. Department of Physics, University of Oslo, N-0316 Oslo, Norway;1. National Engineering Research Center for Advanced Polymer Processing Technology, Zhengzhou University, Zhengzhou, Henan, 450002, China;2. College of Materials Science and Engineering, Zhengzhou University, Zhengzhou, Henan, 450001, China;3. School of Mechanical and Electrical Engineering, Zhoukou Normal University, Zhoukou, Henan, 466001 China;4. School of Urban Planning and Architecture, Southwest Minzu University, Chengdu 610041, China;5. Integrated Composites Laboratory (ICL), Department of Chemical & Biomolecular Engineering, University of Tennessee, Knoxville, TN, 37996, USA;6. School of Material Science and Engineering, Jiangsu University of Science and Technology, Zhenjiang, Jiangsu, 212003, China;7. State Key Laboratory of Marine Resource Utilization in South China Sea, Hainan University, Haikou, China;1. Université Grenoble Alpes, Institut Neel, 25 Rue des Martyr, F-38042 Grenoble, France;2. CNRS, Institut Néel, F-38042 Grenoble, France |
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| Abstract: | We present the systematic treatment of multiple integrals over a simplex of the dimensionality d (d-simplex). The integrand is an analytical function in a suitable domain, and the linear form was employed as an argument. Using the elements obtained from the values of the integrand at the vertices of the d-simplex, integral can be evaluated analytically and expressed as the quotient of two determinants. Potential applications of the results described in the present study include numerical computations of Green?s function (GF), and the response of quantum systems in terms of complex susceptibilities in multidimensional space. |
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