{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","description":"This cluster of papers focuses on the development and application of multiscale methods for analyzing heterogeneous systems, particularly in the context of homogenization, finite element simulations, and porous media flow. The papers cover topics such as upscaling techniques, subsurface flow simulation, coarse-grained computation, and the use of microscopic simulators to perform system-level analysis.","keywords":[{"id":"https://openalex.org/keywords/two-scale-convergence","display_name":"two-scale convergence","score":0.8858},{"id":"https://openalex.org/keywords/computational-homogenization","display_name":"computational homogenization","score":0.2164},{"id":"https://openalex.org/keywords/stochastic-homogenization","display_name":"stochastic homogenization","score":0.5527},{"id":"https://openalex.org/keywords/periodic-homogenization","display_name":"periodic homogenization","score":0.5971},{"id":"https://openalex.org/keywords/periodic-microstructure","display_name":"periodic microstructure","score":0.2044},{"id":"https://openalex.org/keywords/perforated-domains","display_name":"perforated domains","score":0.588},{"id":"https://openalex.org/keywords/multiscale-methods","display_name":"multiscale methods","score":0.2351},{"id":"https://openalex.org/keywords/multiscale-finite-element-method","display_name":"multiscale finite element method","score":0.4851},{"id":"https://openalex.org/keywords/multiscale-problems","display_name":"multiscale problems","score":0.3195},{"id":"https://openalex.org/keywords/periodic-media","display_name":"periodic media","score":0.2148},{"id":"https://openalex.org/keywords/cell-problems","display_name":"cell problems","score":0.6594},{"id":"https://openalex.org/keywords/rapidly-oscillating-coefficients","display_name":"rapidly oscillating coefficients","score":0.5937},{"id":"https://openalex.org/keywords/atomistic-to-continuum-coupling","display_name":"atomistic-continuum coupling","score":0.2452},{"id":"https://openalex.org/keywords/correctors","display_name":"correctors","score":0.4464},{"id":"https://openalex.org/keywords/effective-coefficients","display_name":"effective coefficients","score":0.5787},{"id":"https://openalex.org/keywords/oscillatory-coefficients","display_name":"oscillating coefficients","score":0.3845},{"id":"https://openalex.org/keywords/heterogeneous-multiscale-method","display_name":"heterogeneous multiscale method","score":0.7504},{"id":"https://openalex.org/keywords/homogenization-theory","display_name":"homogenization theory","score":0.2134},{"id":"https://openalex.org/keywords/multiscale-basis-functions","display_name":"multiscale basis functions","score":0.6998},{"id":"https://openalex.org/keywords/generalized-multiscale-finite-element-method","display_name":"generalized multiscale finite element method","score":0.7423},{"id":"https://openalex.org/keywords/multiscale-homogenization","display_name":"multiscale homogenization","score":0.2323},{"id":"https://openalex.org/keywords/effective-equations","display_name":"effective equations","score":0.4121},{"id":"https://openalex.org/keywords/two-scale-homogenization","display_name":"two-scale homogenization","score":0.4334},{"id":"https://openalex.org/keywords/homogenized-coefficients","display_name":"homogenized coefficients","score":0.8356},{"id":"https://openalex.org/keywords/periodically-perforated-domains","display_name":"periodically perforated domains","score":0.8104}],"legacy_keywords":"Multiscale Methods; Heterogeneous; Homogenization; Finite Element; Porous Media; Elliptic Problems; Upscaling Techniques; Subsurface Flow; Coarse-Grained Computation; Microscopic Simulators","ids":{"openalex":"https://openalex.org/T12100","wikipedia":"https://en.wikipedia.org/wiki/Multiscale_modeling"},"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"},"siblings":[{"id":"https://openalex.org/T10142","display_name":"Formal Methods in Verification"},{"id":"https://openalex.org/T10211","display_name":"Computational Drug Discovery Methods"},{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research"},{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis"},{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs"},{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms"},{"id":"https://openalex.org/T10848","display_name":"Advanced Multi-Objective Optimization Algorithms"},{"id":"https://openalex.org/T11063","display_name":"Rough Sets and Fuzzy Logic"},{"id":"https://openalex.org/T11125","display_name":"Petri Nets in System Modeling"},{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation"},{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory"},{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms"},{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic"},{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms"},{"id":"https://openalex.org/T12162","display_name":"Cellular Automata and Applications"},{"id":"https://openalex.org/T12469","display_name":"Chaos, Complexity, and Education"},{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis"},{"id":"https://openalex.org/T12541","display_name":"Graph Labeling and Dimension Problems"},{"id":"https://openalex.org/T12794","display_name":"Adaptive Dynamic Programming Control"},{"id":"https://openalex.org/T12809","display_name":"Contact Mechanics and Variational Inequalities"},{"id":"https://openalex.org/T13182","display_name":"Quantum-Dot Cellular Automata"},{"id":"https://openalex.org/T13286","display_name":"Modeling and Simulation Systems"},{"id":"https://openalex.org/T13523","display_name":"Mathematics, Computing, and Information Processing"}],"works_count":21928,"cited_by_count":270671,"works_api_url":"https://api.openalex.org/works?filter=topics.id:T12100","updated_date":"2026-10-21T03:01:35","created_date":"2024-01-23T15:27:13"}