Wriggers, P., Computational Contact Mechanics. 2006, Springer Berlin Heidelberg, 1–518.
Wriggers, P., Vu Van, T., Stein, E., Finite element formulation of large deformation impact-contact problems with friction. Comput. Struct. 37:3 (1990), 319–331.
Zhu, F., Zhao, L., Lu, G., Gad, E., A numerical simulation of the blast impact of square metallic sandwich panels. Int. J. Impact Eng. 36:5 (2009), 687–699.
Ambrosi, D, Ateshian, Gerard A, Arruda, Ellen M, Cowin, SC, Dumais, J, Goriely, A, Holzapfel, Gerhard A, Humphrey, Jay D, Kemkemer, R, Kuhl, Ellen, et al. Perspectives on biological growth and remodeling. J. Mech. Phys. Solids 59:4 (2011), 863–883.
Dvorkin, Eduardo N., PETÖCZ, E.V.A. G., An effective technique for modelling 2D metal forming processes using an Eulerian formulation. Eng. Comput., 1993.
Berazategui, Diego A, Cavaliere, Miguel A, Montelatici, Luca, Dvorkin, Eduardo N, On the modelling of complex 3D bulk metal forming processes via the pseudo-concentrations technique. Application to the simulation of the mannesmann piercing process. Internat. J. Numer. Methods Engrg. 65:7 (2006), 1113–1144.
Al-Athel, K.S., Gadala, M.S., Eulerian volume of solid (VOS) approach in solid mechanics and metal forming. Comput. Methods Appl. Mech. Engrg. 200:25–28 (2011), 2145–2159.
Boman, R., Papeleux, L., Bui, Q.V., Ponthot, J.P., Application of the arbitrary Lagrangian Eulerian formulation to the numerical simulation of cold roll forming process. J. Mater Process. Technol. 177:1 (2006), 621–625 Proceedings of the 11th International Conference on Metal Forming 2006.
Camacho, G.T., Ortiz, M., Adaptive Lagrangian modelling of ballistic penetration of metallic targets. Comput. Methods Appl. Mech. Engrg. 142:3 (1997), 269–301.
Roarty, Colleen M., Grosland, Nicole M., Adaptive meshing technique applied to an orthopaedic finite element contact problem. Iowa Orthop. J., 24, 2004, 21.
Zeramdini, Bessam, Robert, Camille, Germain, Guenael, Pottier, Thomas, Numerical simulation of metal forming processes with 3D adaptive remeshing strategy based on a posteriori error estimation. Int. J. Mater. Form. 12:3 (2019), 411–428.
Chen, Jiun-Shyan, Hillman, Michael, Chi, Sheng-Wei, Meshfree methods: progress made after 20 years. J. Eng. Mech., 143(4), 2017, 04017001.
Gingold, Robert A., Monaghan, Joseph J., Smoothed particle hydrodynamics: theory and application to non-spherical stars. Mon. Not. R. Astron. Soc. 181:3 (1977), 375–389.
Li, Bo, Habbal, Feras, Ortiz, Michael, Optimal transportation meshfree approximation schemes for fluid and plastic flows. Internat. J. Numer. Methods Engrg. 83:12 (2010), 1541–1579.
Sukumar, Natarajan, Moran, Brian, Belytschko, Ted, The natural element method in solid mechanics. Internat. J. Numer. Methods Engrg. 43:5 (1998), 839–887.
Yvonnet, Julien, Ryckelynck, David, Lorong, Philippe, Chinesta, Francisco, A new extension of the natural element method for non-convex and discontinuous problems: the constrained natural element method (c-NEM). Internat. J. Numer. Methods Engrg. 60:8 (2004), 1451–1474.
Liu, Wing Kam, Jun, Sukky, Zhang, Yi Fei, Reproducing kernel particle methods. Internat. J. Numer. Methods Fluids 20:8–9 (1995), 1081–1106.
Atluri, Satya N., Zhu, Tulong, A new meshless local Petrov-Galerkin (MLPG) approach in computational mechanics. Comput. Mech. 22:2 (1998), 117–127.
Melenk, J.M., Babuška, I., The partition of unity finite element method: Basic theory and applications. Comput. Methods Appl. Mech. Engrg. 139:1 (1996), 289–314.
Lu, Y.Y., Belytschko, T., Gu, Lu, A new implementation of the element free Galerkin method. Comput. Methods Appl. Mech. Engrg. 113:3–4 (1994), 397–414.
Cockburn, Bernardo, Karniadakis, George E., Shu, Chi-Wang, The development of discontinuous Galerkin methods. Discontinuous Galerkin Methods, 2000, Springer, 3–50.
Deeks, Andrew J., Augarde, Charles E., A meshless local Petrov-Galerkin scaled boundary method. Comput. Mech. 36:3 (2005), 159–170.
Ullah, Zahur, Augarde, C.E., Finite deformation elasto-plastic modelling using an adaptive meshless method. Comput. Struct. 118 (2013), 39–52.
Boroomand, Bijan, Parand, Sina, Towards a general interpolation scheme. Comput. Methods Appl. Mech. Engrg., 381, 2021, 113830.
Sukumar, N., Construction of polygonal interpolants: a maximum entropy approach. Internat. J. Numer. Methods Engrg. 61:12 (2004), 2159–2181.
Arroyo, Marino, Ortiz, Michael, Local maximum-entropy approximation schemes: a seamless bridge between finite elements and meshfree methods. Internat. J. Numer. Methods Engrg. 65:13 (2006), 2167–2202.
Askes, Harm, de Borst, René, Heeres, Otto, Conditions for locking-free elasto-plastic analyses in the element-free Galerkin method. Comput. Methods Appl. Mech. Engrg. 173:1–2 (1999), 99–109.
Belytschko, Ted, Organ, D., Krongauz, Y., A coupled finite element-element-free Galerkin method. Comput. Mech. 17:3 (1995), 186–195.
Huerta, Antonio, Fernández-Méndez, Sonia, Enrichment and coupling of the finite element and meshless methods. Internat. J. Numer. Methods Engrg. 48:11 (2000), 1615–1636.
Huerta, Antonio, Fernández-Méndez, Sonia, Liu, Wing Kam, A comparison of two formulations to blend finite elements and mesh-free methods. Comput. Methods Appl. Mech. Engrg. 193:12 (2004), 1105–1117 Meshfree Methods: Recent Advances and New Applications.
Hegen, D., Element-free Galerkin methods in combination with finite element approaches. Comput. Methods Appl. Mech. Engrg. 135:1 (1996), 143–166.
Rabczuk, Timon, Belytschko, Ted, Application of particle methods to static fracture of reinforced concrete structures. Int. J. Fract. 137:1 (2006), 19–49.
Gu, Y.T., Zhang, L.C., Coupling of the meshfree and finite element methods for determination of the crack tip fields. Eng. Fract. Mech. 75:5 (2008), 986–1004.
Xiao, Q.Z., Dhanasekar, M., Coupling of FE and EFG using collocation approach. Adv. Eng. Softw. 33:7 (2002), 507–515 Engineering Computational Technology & Computational Structures Technology.
Rabczuk, Timon, Xiao, Shao Ping, Sauer, M., Coupling of mesh-free methods with finite elements: basic concepts and test results. Commun. Numer. Methods. Eng. 22:10 (2006), 1031–1065.
Ullah, Zahur, Augarde, Charles E, Crouch, Roger S, Coombs, William M, FE-EFGM coupling using maximum entropy shape functions and its application to small and finite deformation. 2011.
Ullah, Zahur, Augarde, C.E., Coombs, W.M., Local maximum entropy shape functions based FE-EFGM coupling. 2013.
Ullah, Z., Coombs, W.M., Augarde, C.E., An adaptive finite element/meshless coupled method based on local maximum entropy shape functions for linear and nonlinear problems. Comput. Methods Appl. Mech. Engrg. 267 (2013), 111–132.
Babuška, Ivo, The finite element method with Lagrangian multipliers. Numer. Math. 20:3 (1973), 179–192.
Magoulès, Frédéric, Roux, François-Xavier, Lagrangian formulation of domain decomposition methods: A unified theory. Appl. Math. Model. 30:7 (2006), 593–615 Parallel and Vector Processing in Science and Engineering.
Wohlmuth, Barbara I., A mortar finite element method using dual spaces for the Lagrange multiplier. SIAM J. Numer. Anal. 38:3 (2000), 989–1012.
Bernardi, Christine, Maday, Yvon, Patera, Anthony T., Domain decomposition by the mortar element method. Asymptotic and Numerical Methods for Partial Differential Equations with Critical Parameters, 1993, Springer, 269–286.
Nitsche, Joachim, Über ein variationsprinzip zur lösung von Dirichlet-problemen bei verwendung von teilräumen, die keinen randbedingungen unterworfen sind. Abhandlungen Aus Dem Mathematischen Seminar Der Universität Hamburg, Vol. 36, 1971, Springer, 9–15.
Becker, Roland, Hansbo, Peter, Stenberg, Rolf, A finite element method for domain decomposition with non-matching grids. ESAIM Math. Model. Numer. Anal. 37:2 (2003), 209–225.
Ullah, Zahur, Coombs, Will, Augarde, C., Parallel computations in nonlinear solid mechanics using adaptive finite element and meshless methods. Eng. Comput., 2016.
Vacharasintopchai, Thiti, A parallel implementation of the element-free Galerkin method on a network of PCs. (Ph.D. thesis), 2000, Asian Institute of Technology.
Singh, Indra Vir, Jain, P.K., Parallel EFG algorithm for heat transfer problems. Adv. Eng. Softw. 36:8 (2005), 554–560.
Karutz, H., Chudoba, R., Krätzig, W.B., Automatic adaptive generation of a coupled finite element/element-free Galerkin discretization. Finite Elem. Anal. Des. 38:11 (2002), 1075–1091.
Wriggers, Peter, Nonlinear Finite Element Methods. 2008, Springer Science & Business Media.
Krongauz, Y., Belytschko, T., Enforcement of essential boundary conditions in meshless approximations using finite elements. Comput. Methods Appl. Mech. Engrg. 131:1 (1996), 133–145.
Zhu, T., Atluri, SN1633725, A modified collocation method and a penalty formulation for enforcing the essential boundary conditions in the element free Galerkin method. Comput. Mech. 21:3 (1998), 211–222.
Zienkiewicz, Olgierd Cecil, Taylor, Robert Leroy, Zhu, Jian Z., The Finite Element Method: Its Basis and Fundamentals. 2005, Elsevier.
Kirby, Robert C., Mitchell, Lawrence, Code generation for generally mapped finite elements. ACM Trans. Math. Softw. 45:4 (2019), 1–23.
Sukumar, N., Wright, R.W., Overview and construction of meshfree basis functions: from moving least squares to entropy approximants. Internat. J. Numer. Methods Engrg. 70:2 (2007), 181–205.
Bishop, Joseph, A kinematic comparison of meshfree and mesh-based Lagrangian approximations using manufactured extreme deformation fields. Comput. Part. Mech. 7:2 (2020), 257–270.
Duan, Qinglin, Li, Xikui, Zhang, Hongwu, Belytschko, Ted, Second-order accurate derivatives and integration schemes for meshfree methods. Internat. J. Numer. Methods Engrg. 92:4 (2012), 399–424.
Karypis, George, Kumar, Vipin, METIS: A software package for partitioning unstructured graphs, partitioning meshes, and computing fill-reducing orderings of sparse matrices. 1997.
Balay, Satish, Abhyankar, Shrirang, Adams, Mark F., Benson, Steven, Brown, Jed, Brune, Peter, Buschelman, Kris, Constantinescu, Emil M., Dalcin, Lisandro, Dener, Alp, Eijkhout, Victor, Gropp, William D., Hapla, Václav, Isaac, Tobin, Jolivet, Pierre, Karpeev, Dmitry, Kaushik, Dinesh, Knepley, Matthew G., Kong, Fande, Kruger, Scott, May, Dave A., McInnes, Lois Curfman, Mills, Richard Tran, Mitchell, Lawrence, Munson, Todd, Roman, Jose E., Rupp, Karl, Sanan, Patrick, Sarich, Jason, Smith, Barry F., Zampini, Stefano, Zhang, Hong, Zhang, Hong, Zhang, Junchao, PETSc web page. 2021 URL https://petsc.org/.
Balay, Satish, Abhyankar, Shrirang, Adams, Mark F., Benson, Steven, Brown, Jed, Brune, Peter, Buschelman, Kris, Constantinescu, Emil, Dalcin, Lisandro, Dener, Alp, Eijkhout, Victor, Gropp, William D., Hapla, Václav, Isaac, Tobin, Jolivet, Pierre, Karpeev, Dmitry, Kaushik, Dinesh, Knepley, Matthew G., Kong, Fande, Kruger, Scott, May, Dave A., McInnes, Lois Curfman, Mills, Richard Tran, Mitchell, Lawrence, Munson, Todd, Roman, Jose E., Rupp, Karl, Sanan, Patrick, Sarich, Jason, Smith, Barry F., Zampini, Stefano, Zhang, Hong, Zhang, Hong, Zhang, Junchao, PETSc/TAO Users Manual: Technical Report ANL-21/39 - Revision 3.16., 2021, Argonne National Laboratory.
Balay, Satish, Gropp, William D., McInnes, Lois Curfman, Smith, Barry F., Efficient management of parallelism in object oriented numerical software libraries. Arge, E., Bruaset, A.M., Langtangen, H.P., (eds.) Modern Software Tools in Scientific Computing, 1997, Birkhäuser Press, 163–202.
Timoshenko, Stephen, Goodier, James Norman, Theory of Elasticity: By S. Timoshenko and JN Goodier. 1951, McGraw-Hill.
Rosolen, Adrian, Millán, Daniel, Arroyo, Marino, On the optimum support size in meshfree methods: a variational adaptivity approach with maximum-entropy approximants. Internat. J. Numer. Methods Engrg. 82:7 (2010), 868–895.
Mamou, Khaled, Volumetric hierarchical approximate convex decomposition. Game Engine Gems 3, 2016, A K Peters, 141–158.
Gene M. Amdahl, Validity of the single processor approach to achieving large scale computing capabilities, in: Proceedings of the April 18-20, 1967, Spring Joint Computer Conference, 1967, pp. 483–485.
Goriely, A., The Mathematics and Mechanics of Biological Growth. 2017, Springer.
Cuitino, Alberto, Ortiz, M., A material-independent method for extending stress update algorithms from small-strain plasticity to finite plasticity with multiplicative kinematics. Eng. Comput. 9:4 (1992), 437–451.
