REFERENCES
- Bathe, K.-J. (2006). Finite Element Procedures, Upper Saddle River, NJ: Prentice Hall.
- Belytschko, T., Krongauz, Y., Organ, D., Fleming, M., Krysl, P. (1996). Meshless methods: An overview and recent developments. Computer Methods in Applied Mechanics and Engineering 139:3–47. doi:10.1016/s0045-7825(96)01078-x
- Belytschko, T., Lu, Y. Y., Gu, L. (1994). Element free Galerkin methods. International Journal for Numerical Methods in Engineering 37:229–256.
- Bernstein, D. S. (2009). Matrix Mathematics: Theory, Facts, and Formulas. Princeton, NJ: Princeton University Press.
- Concus, P., Golub, G. H. (1973). Use of fast direct methods for the efficient numerical solution of nonseparable elliptic equations. SIAM Journal on Numerical Analysis 10:1103–1120. doi:10.1137/0710092
- Davie, A. M., Stothers, A. J. (2013). Improved bound for complexity of matrix multiplication. Proceedings of the Royal Society of Edinburgh: Section A Mathematics 143:351–369. doi:10.1017/s0308210511001648
- Demirhan, N., Kanber, B. (2013). Finite element analysis of frictional contacts of FGM coated elastic members. Mechanics Based Design of Structures and Machines 41:383–398. doi:10.1080/15397734.2012.722882
- Duarte, C. A., Oden, J. (1995). A Review of Some Meshless Methods to Solve Partial Differential Equations. Austin, TX: Texas Institute for Computational and Applied Mathematics.
- El Hami, A., Radi, B. (1996). Some decomposition methods in the analysis of repetitive structures. Computers & Structures 58:973–980. doi:10.1016/0045-7949(95)00206-v
- Farhat, C. (1991). A Lagrange multiplier based divide and conquer finite element algorithm. Computing Systems in Engineering 2:149–156. doi:10.1016/0956-0521(91)90015-w
- Fries, T.-P., Matthies, H.-G. (2003). Classification and Overview of Meshfree Methods. Braunschweig, Germany: Department of Mathematics and Computer Science, Technical University of Braunschweig.
- Golub, G. H., Van Loan, C. F. (2012). Matrix Computations. Baltimore, MD: Johns Hopkins University Press. 0801854148, 978080 1854149.
- Greengard, L., Rokhlin, V. (1997). A new version of the fast multipole method for the Laplace equation in three dimensions. Acta Numerica 6:229–269. doi:10.1017/s0962492900002725
- Griebel, M., Schweitzer, M. A. (2005). Meshfree Methods for Partial Differential Equations II. Berlin, Heidelberg, Germany: Springer.
- Gu, Y. (2005). Meshfree methods and their comparisons. International Journal of Computational Methods 2:477–515. doi:10.1142/s0219876205000673
- Kaveh, A. (2013). Optimal Analysis of Structures by Concepts of Symmetry and Regularity. Wien-NewYork: Springer Verlag GmbH.
- Kaveh, A., Mahdavi, V. R. (2015). Optimal domain decomposition using Colliding Bodies Optimization and k-median method. Finite Elements in Analysis and Design 98:41–49. doi:10.1016/j.finel.2015.01.010
- Kaveh, A., Rahami, H. (2010). An efficient analysis of repetitive structures generated by graph products. International Journal for Numerical Methods in Engineering 84:108–126. doi:10.1002/nme.2893
- Kaveh, A., Shojaei, I., Rahami, H. (2014). New developments in the optimal analysis of regular and near-regular structures: Decomposition, graph products, force method. Acta Mechanica 226:665–681. doi:10.1007/s00707-014-1194-1
- Kennedy, G. J., Martins, J. R. (2014). A parallel finite-element framework for large-scale gradient-based design optimization of high-performance structures. Finite Elements in Analysis and Design 87:56–73. doi:10.1016/j.finel.2014.04.011
- Le Gall, F. (2014). Powers of Tensors and Fast Matrix Multiplication. Proceedings of the 39th International Symposium on Symbolic and Algebraic Computation, New York: ACM Press, 296–303.
- Li, H., Schindler, C. (2013). Investigation of tire-soil interaction with analytical and finite element method. Mechanics Based Design of Structures and Machines 41:293–315. doi:10.1080/15397734.2012.744677
- Liao, A., Zhang, H., Wu, C. (2007). A finite element model for 3D elastoplastic frictional contact analysis and its application in numerical simulation of turbocharger compressor. Mechanics Based Design of Structures and Machines 35:267–289. doi:10.1080/15397730701404684
- Liu, G.-R. (2009). Meshfree Methods: Moving Beyond the Finite Element Method. Boca Raton, FL: CRC Press. 1420082108, 9781420082104.
- Mandel, J. (1990). Iterative solvers by substructuring for the p-version finite element method. Computer Methods in Applied Mechanics and Engineering 80:117–128. doi:10.1016/0045-7825(90)90017-g
- Molano, R., Rodríguez, P. G., Caro, A., Durán, M. L. (2012). Finding the largest area rectangle of arbitrary orientation in a closed contour. Applied Mathematics and Computation 218:9866–9874. doi:10.1016/j.amc.2012.03.063
- Oñate, E., Idelsohn, S., Zienkiewicz, O., Taylor, R. (1996). A finite point method in computational mechanics. Applications to convective transport and fluid flow. International Journal for Numerical Methods in Engineering 39:3839–3866. doi:10.1002/(sici)1097-0207(19961130)39:223.0.co;2-r
- Oñate, E., Idelsohn, S., Zienkiewicz, O., Taylor, R., Sacco, C. (1996). A stabilized finite point method for analysis of fluid mechanics problems. Computer Methods in Applied Mechanics and Engineering 139:315–346. doi:10.1016/s0045-7825(96)01088-2
- Pothen, A., Simon, H. D., Liou, K.-P. (1990). Partitioning sparse matrices with eigenvectors of graphs. SIAM Journal on Matrix Analysis and Applications 11:430–452. doi:10.1137/0611030
- Rabczuk, T., Areias, P., Belytschko, A. (2007). Meshfree thin shell method for non-linear dynamic fracture. International Journal for Numerical Methods in Engineering 72:524–648. doi:10.1002/nme.2013
- Shojaei, I., Kaveh, A., Rahami, H. (2013). Analysis of structures convertible to repeated structures using graph products. Computers & Structures 125:153–163. doi:10.1016/j.compstruc.2013.04.018
- Shojaei, I., Rahami, H., Kaveh, A. (2015). Efficient finite element solution of regular and near-regular systems using graph products. Acta Mechanica 226:2393–2405. doi:10.1007/s00707-015-1337-z
- Silling, S. A., Askari, E. (2005). A meshfree method based on the peridynamic model of solid mechanics. Computers & Structures 83:1526–1535. doi:10.1016/j.compstruc.2004.11.026
- Sluzalec, A. (2012). Stochastic finite elements in optimization of powder metallurgy materials. Mechanics Based Design of Structures and Machines 40:33–41. doi:10.1080/15397734.2011.598110
- Spitas, C., Spitas, V. (2007). A FEM study of the bending strength of circular fillet gear teeth compared to trochoidal fillets produced with enlarged cutter tip radius. Mechanics Based Design of Structures and Machines 35:59–73. doi:10.1080/15397730601182802
- Szilard, R. (2004). Theories and Applications of Plate Analysis: Classical Numerical and Engineering Methods. Hoboken, NJ: John Wiley & Sons, Inc..
- Xiu, D. (2009). Fast numerical methods for stochastic computations: A review. Communications in Computational Physics 5:242–272.
- Yavari, A., Kaveh, A., Sarkani, S., Rahimi Bondarabady, H. A. (2001). Topological aspects of meshless methods and nodal ordering for meshless discretization. International Journal for Numerical Methods in Engineering 52:921–938.
- Zingoni, A. (2009). Group–theoretic exploitations of symmetry in computational solid and structural mechanics. International Journal for Numerical Methods in Engineering 79:253–289. doi:10.1002/nme.2576