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Numerical simulation of the temperature field of the stadium building foundation in frozen areas based on the finite element method and proper orthogonal decomposition technique
Author(s) -
Song Zhengyuan,
Li Huanrong
Publication year - 2021
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.7275
Subject(s) - proper orthogonal decomposition , finite element method , mathematics , stadium , field (mathematics) , point of delivery , computer simulation , foundation (evidence) , numerical analysis , mathematical analysis , structural engineering , geometry , engineering , statistics , geography , archaeology , pure mathematics , agronomy , biology
This paper is mainly concerned with the development and design of a reduced order model in numerical simulation of the unsteady temperature field of the stadium building foundation in frozen areas, based the finite element (FE) method and proper orthogonal decomposition (POD) with the snapshot technique. We first derive the standard FE formulation of the unsteady temperature field and compute its FE full solutions, from which we choose a few spatio‐temporal solutions as snapshots. Based on POD technique, we then build a set of optimal POD bases maximizing the energy content in the original ensemble data, and in the new space spanned by the POD basis, we establish a low‐order numerical model of reduced‐order finite element (ROFE) formulation of the unsteady temperature field. And we prove the error estimates of the ROFE solutions of the unsteady temperature field. Finally, numerical tests are provided to simulate the temperature field of crushed stone clay under the natural pavement near the foundation of a stadium building in a frozen soil area of the northwest of Sichuan province in China.