Most cited papers in Advanced Mathematical Modeling in Engineering
What are the most cited papers in Advanced Mathematical Modeling in Engineering?
The most cited paper in Advanced Mathematical Modeling in Engineering is "Generating optimal topologies in structural design using a homogenization method" (Martin Philip Bendsøe, Noboru Kikuchi, 1988), with 7,508 citations. Next come "Elastic properties of reinforced solids: Some theoretical principles" (4,905) and "Perturbation Methods" (4,699).
Showing 50 of 100 papers. Every paper with more than 900 citations is listed.
| # | Paper | ||
|---|---|---|---|
| 1 | Generating optimal topologies in structural design using a homogenization method Martin Philip Bendsøe, Noboru Kikuchi · Computer Methods in Applied Mechanics and Engineering | Nov 1988 | 7,508 |
| 2 | Elastic properties of reinforced solids: Some theoretical principles R. Hill · Journal of the Mechanics and Physics of Solids | Sep 1963 | 4,905 |
| 3 | Perturbation Methods A. H. Nayfeh, Vimal Singh · IEEE Transactions on Systems Man and Cybernetics | May 1978 | 4,699 |
| 4 | Optimal shape design as a material distribution problem Martin Philip Bendsøe · Structural and Multidisciplinary Optimization | Dec 1989 | 4,565 |
| 5 | Compact sets in the spaceL p (O,T; B) Jacques Simon · Annali di Matematica Pura ed Applicata (1923 -) | Dec 1986 | 4,138 |
| 6 | Stochastic Differential Equations and Diffusion Processes Gopinath Kallianpur, Nobuyuki Ikeda, Shinzo Watanabe · Technometrics | May 1983 | 3,919 |
| 7 | Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I Shmuel Agmon, Avron Douglis, Louis Nirenberg · Communications on Pure and Applied Mathematics | Nov 1959 | 3,784 |
| 8 | Large Deviations Techniques and Applications Uwe Schmock, Amir Dembo, Ofer Zeitouni · Journal of the American Statistical Association | Dec 2000 | 3,718 |
| 9 | A self-consistent mechanics of composite materials R. Hill · Journal of the Mechanics and Physics of Solids | Aug 1965 | 3,692 |
| 10 | The partition of unity finite element method: Basic theory and applications Jens Markus Melenk, Ivo M. Babuska · Computer Methods in Applied Mechanics and Engineering | Dec 1996 | 3,457 |
| 11 | Mixed finite elements in ?3 Jean-Claude Nédélec · Numerische Mathematik | Sep 1980 | 3,304 |
| 12 | Positive solutions of nonlinear elliptic equations involving critical sobolev exponents Haïm Brézis, Louis Nirenberg · Communications on Pure and Applied Mathematics | Jul 1983 | 2,942 |
| 13 | Thermodynamically consistent phase‐field models of fracture: Variational principles and multi‐field FE implementations Christian Miehé, Fabian Welschinger, Martina Hofacker · International Journal for Numerical Methods in Engineering | 22 Mar 2010 | 2,938 |
| 14 | Symmetry and related properties via the maximum principle Basilis Gidas, Wei‐Ming Ni, Louis Nirenberg · Communications in Mathematical Physics | Oct 1979 | 2,934 |
| 15 | Fourier integral operators. I Lars Hörmander · Acta Mathematica | 1971 | 2,434 |
| 16 | A Multiphase Level Set Framework for Image Segmentation Using the Mumford and Shah Model Luminita A. Vese, Tony Fan-Cheong Chan · International Journal of Computer Vision | Dec 2002 | 2,394 |
| 17 | A Model for Boundary Diffusion Controlled Creep in Polycrystalline Materials ROBERT L. COBLE · Journal of Applied Physics | Jun 1963 | 2,332 |
| 18 | Level Set Methods: An Overview and Some Recent Results Stanley Osher, Ronald P. Fedkiw · Journal of Computational Physics | May 2001 | 2,308 |
| 19 | Homogenization and Two-Scale Convergence Grégoire Allaire · SIAM Journal on Mathematical Analysis | Nov 1992 | 2,295 |
| 20 | Image Selective Smoothing and Edge Detection by Nonlinear Diffusion. II Luis Álvarez, Pierre-Louis Lions, Jean‐Michel Morel · SIAM Journal on Numerical Analysis | Jun 1992 | 2,221 |
| 21 | Numerical instabilities in topology optimization: A survey on procedures dealing with checkerboards, mesh-dependencies and local minima Ole Sigmund, Joakim H. Petersson · Structural and Multidisciplinary Optimization | Aug 1998 | 2,128 |
| 22 | An extension problem related to the fractional Laplacian Luis A. Caffarelli, Luís Silvestre | 2006 | 2,125 |
| 23 | A relation between pointwise convergence of functions and convergence of functionals Haïm Brézis, Élliott H. Lieb · Proceedings of the American Mathematical Society | Jul 1983 | 2,089 |
| 24 | Commutator estimates and the euler and navier‐stokes equations Tosio Kato, Gustavo Henrique Santos Flores Ponce · Communications on Pure and Applied Mathematics | Oct 1988 | 1,919 |
| 25 | A phase-field description of dynamic brittle fracture Michael J. Borden, Clemens V. Verhoosel, Michael A. Scott et al. · Computer Methods in Applied Mechanics and Engineering | 26 Jan 2012 | 1,914 |
| 26 | A Multiscale Finite Element Method for Elliptic Problems in Composite Materials and Porous Media Thomas Y. Hou, Xiaohui Wu · Journal of Computational Physics | Jun 1997 | 1,909 |
| 27 | Domain decomposition: Parallel multilevel methods for elliptic partial differential equations By Barry Smith · Computers & Mathematics with Applications | Feb 1997 | 1,870 |
| 28 | Perturbation Methods in Applied Mathematics Julian D. Cole, Lawrence Elliott Levine · IEEE Transactions on Systems Man and Cybernetics | Nov 1973 | 1,842 |
| 29 | Multiscale phenomena: Green's functions, the Dirichlet-to-Neumann formulation, subgrid scale models, bubbles and the origins of stabilized methods Thomas J.R. Hughes · Computer Methods in Applied Mechanics and Engineering | Nov 1995 | 1,798 |
| 30 | On the elastic moduli of some heterogeneous materials Bernard Budiansky · Journal of the Mechanics and Physics of Solids | Aug 1965 | 1,703 |
| 31 | Asymptotic Analysis of Periodic Structures Alain Bensoussan, J. L. Lions, George Papanicolaou et al. · Journal of Applied Mechanics | Jun 1979 | 1,697 |
| 32 | The Concentration-Compactness Principle in the Calculus of Variations. The Limit Case, Part 2 Pierre-Louis Lions · Revista Matemática Iberoamericana | 30 Jun 1985 | 1,695 |
| 33 | The variational multiscale method—a paradigm for computational mechanics Thomas J.R. Hughes, Gonzalo R. Feijóo, Luca Mazzei et al. · Computer Methods in Applied Mechanics and Engineering | Nov 1998 | 1,672 |
| 34 | On the Spaces Lp(x)(Ω) and Wm,p(x)(Ω) Xianling Fan, Dun Zhao · Journal of Mathematical Analysis and Applications | Nov 2001 | 1,624 |
| 35 | The concentration-compactness principle in the Calculus of Variations. The Locally compact case, part 2 Pierre‐Louis Lions · Annales de l Institut Henri Poincaré C Analyse Non Linéaire | Aug 1984 | 1,583 |
| 36 | New tight frames of curvelets and optimal representations of objects with piecewise C 2 singularities Emmanuel J. Candès, David L. Donoho · Communications on Pure and Applied Mathematics | 14 Nov 2003 | 1,581 |
| 37 | THE GEOMETRY OF DISSIPATIVE EVOLUTION EQUATIONS: THE POROUS MEDIUM EQUATION Félix Otto · Communications in Partial Differential Equations | 31 Jan 2001 | 1,567 |
| 38 | On the parabolic kernel of the Schrödinger operator Peter Li, Shing Tung Yau · Acta Mathematica | 1986 | 1,566 |
| 39 | Diffusion Models: A Comprehensive Survey of Methods and Applications Ling Qiang Yang, Zhilong Zhang, Yang Song et al. · ACM Computing Surveys | 30 Sep 2023 | 1,565 |
| 40 | Pyramidal implementation of the Lucas Kanade feature tracker description of the algorithm J.-Y. Bouguet | 1999 | 1,561 |
| 41 | Regularity for a more general class of quasilinear elliptic equations Peter Tolksdorf · Journal of Differential Equations | 1984 | 1,541 |
| 42 | Fine phase mixtures as minimizers of energy John Macleod Ball, Richard D. James · Archive for Rational Mechanics and Analysis | 1987 | 1,519 |
| 43 | Über ein Variationsprinzip zur Lösung von Dirichlet-Problemen bei Verwendung von Teilräumen, die keinen Randbedingungen unterworfen sind Johannes M. Nitsche · Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg | Jul 1971 | 1,476 |
| 44 | The Occurrence of Singularities in the Elastic Frequency Distribution of a Crystal Léon Van Hove · Physical Review | 15 Mar 1953 | 1,467 |
| 45 | A survey of structural and multidisciplinary continuum topology optimization: post 2000 Joshua D. Deaton, Ramana V. Grandhi · Structural and Multidisciplinary Optimization | 3 Jul 2013 | 1,412 |
| 46 | Aggregation vs. global diffusive behavior in the higher-dimensional Keller–Segel model Michael Winkler · Journal of Differential Equations | 22 Feb 2010 | 1,411 |
| 47 | The Concentration-Compactness Principle in the Calculus of Variations. The limit case, Part 1 Pierre‐Louis Lions · Revista Matemática Iberoamericana | 31 Mar 1985 | 1,401 |
| 48 | Elliptic Partial Differential Equations of Second Order Piero Bassanini, Alan R. Elcrat | 1997 | 1,379 |
| 49 | Preprocessing and postprocessing for materials based on the homogenization method with adaptive finite element methods J. M. Guedes, Noboru Kikuchi · Computer Methods in Applied Mechanics and Engineering | Oct 1990 | 1,376 |
| 50 | Uniqueness of positive solutions of Δu−u+up=0 in Rn Man Kam Kwong · Archive for Rational Mechanics and Analysis | Sep 1989 | 1,352 |
Citations are OpenAlex's own counts, from its 2026-09-23 snapshot, so the ranking can differ from Google Scholar or Web of Science. A paper is listed for a field when OpenAlex files it under one of the field's topics; retracted papers and papers whose citation count cannot be traced to citing works are left out, and a preprint and the article it became are shown once. Release dates are OpenAlex's: where a source gave only a month or a year, that is what is shown. How the lists are chosen.