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A radial basis function (RBF) is a real-valued function whose value depends only on the distance between the input and some fixed point,either the origin,so that ,or some other fixed point ,called a center,so that . Any function that satisfies the property is a radial function. The distance is usually Euclidean distance,although other metrics are sometimes used. They are often used as a collection which forms a basis for some function space of interest,hence the name.
In the field of numerical analysis,meshfree methods are those that do not require connection between nodes of the simulation domain,i.e. a mesh,but are rather based on interaction of each node with all its neighbors. As a consequence,original extensive properties such as mass or kinetic energy are no longer assigned to mesh elements but rather to the single nodes. Meshfree methods enable the simulation of some otherwise difficult types of problems,at the cost of extra computing time and programming effort. The absence of a mesh allows Lagrangian simulations,in which the nodes can move according to the velocity field.
A shear band is a narrow zone of intense shearing strain,usually of plastic nature,developing during severe deformation of ductile materials. As an example,a soil specimen is shown in Fig. 1,after an axialsymmetric compression test. Initially the sample was cylindrical in shape and,since symmetry was tried to be preserved during the test,the cylindrical shape was maintained for a while during the test and the deformation was homogeneous,but at extreme loading two X-shaped shear bands had formed and the subsequent deformation was strongly localized.
Johann Hadji Argyris FRS was a Greek pioneer of computer applications in science and engineering,among the creators of the finite element method (FEM),and lately Professor at the University of Stuttgart and Director of the Institute of Structural Mechanics and Dynamics in Aerospace Engineering.
In mathematics,in particular numerical analysis,the FETI method is an iterative substructuring method for solving systems of linear equations from the finite element method for the solution of elliptic partial differential equations,in particular in computational mechanics In each iteration,FETI requires the solution of a Neumann problem in each substructure and the solution of a coarse problem. The simplest version of FETI with no preconditioner in the substructure is scalable with the number of substructures but the condition number grows polynomially with the number of elements per substructure. FETI with a preconditioner consisting of the solution of a Dirichlet problem in each substructure is scalable with the number of substructures and its condition number grows only polylogarithmically with the number of elements per substructure. The coarse space in FETI consists of the nullspace on each substructure.
Thomas Joseph Robert Hughes is a Professor of Aerospace Engineering and Engineering Mechanics and currently holds the Computational and Applied Mathematics Chair (III) at the Oden Institute at The University of Texas at Austin. Hughes has been listed as an ISI Highly Cited Author in Engineering by the ISI Web of Knowledge,Thomson Scientific Company.
MUMPS is a software application for the solution of large sparse systems of linear algebraic equations on distributed memory parallel computers. It was developed in European project PARASOL (1996–1999) by CERFACS,IRIT-ENSEEIHT and RAL. The software implements the multifrontal method,which is a version of Gaussian elimination for large sparse systems of equations,especially those arising from the finite element method. It is written in Fortran 90 with parallelism by MPI and it uses BLAS and ScaLAPACK kernels for dense matrix computations. Since 1999,MUMPS has been supported by CERFACS,IRIT-ENSEEIHT,and INRIA.
The finite element method (FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical modeling. Typical problem areas of interest include the traditional fields of structural analysis,heat transfer,fluid flow,mass transport,and electromagnetic potential.
Klaus-Jürgen Bathe is a civil engineer,professor of mechanical engineering at the Massachusetts Institute of Technology,and founder of ADINA R&D,who specializes in computational mechanics. Bathe is considered to be one of the pioneers in the field of finite element analysis and its applications.
The Center of Excellence (CoE) in Nanotechnology is located inside the Asian Institute of Technology campus. It is one of the eight centers of excellence in Thailand.
Smoothed finite element methods (S-FEM) are a particular class of numerical simulation algorithms for the simulation of physical phenomena. It was developed by combining meshfree methods with the finite element method. S-FEM are applicable to solid mechanics as well as fluid dynamics problems,although so far they have mainly been applied to the former.
False diffusion is a type of error observed when the upwind scheme is used to approximate the convection term in convection–diffusion equations. The more accurate central difference scheme can be used for the convection term,but for grids with cell Peclet number more than 2,the central difference scheme is unstable and the simpler upwind scheme is often used. The resulting error from the upwind differencing scheme has a diffusion-like appearance in two- or three-dimensional co-ordinate systems and is referred as "false diffusion". False-diffusion errors in numerical solutions of convection-diffusion problems,in two- and three-dimensions,arise from the numerical approximations of the convection term in the conservation equations. Over the past 20 years many numerical techniques have been developed to solve convection-diffusion equations and none are problem-free,but false diffusion is one of the most serious problems and a major topic of controversy and confusion among numerical analysts.
Model order reduction (MOR) is a technique for reducing the computational complexity of mathematical models in numerical simulations. As such it is closely related to the concept of metamodeling,with applications in all areas of mathematical modelling.
Ernest Hinton was a British civil engineer and engineering professor. He was born in Liverpool,England in 1946 and was educated at University of Wales Swansea. After receiving the BSc (1967),MSc (1968) and PhD (1971) at Swansea he joined the faculty of the Department of Civil Engineering where served until his death in 1999.
Zhong Zhihua is a Chinese engineer and educator. He served as president of Hunan University from 2005 to 2011,and president of Tongji University from 2016 to 2018. He is a member of the Chinese Academy of Engineering.
Scott William Sloan FRS FREng FAA FTSE was laureate Professor of Civil Engineering at the University of Newcastle.
Kam Tim Chau (周錦添) is an engineering educator. He is an adjunct professor at the Chinese University of Hong Kong and was the Chair Professor in Geotechnical Engineering at The Hong Kong Polytechnic University and was the former President of the Hong Kong Society of Theoretical and Applied Mechanics. He authored three text books in geomechanics and engineering mathematics entitled "Analytic Methods in Geomechanics" (2013) published by CRC Press,"Theory of Differential Equations in Engineering and Mechanics" (2018) published by CRC Press,and "Applications of Differential Equations in Engineering and Mechanics" (2019) also published by CRC Press.
The finite point method (FPM) is a meshfree method for solving partial differential equations (PDEs) on scattered distributions of points. The FPM was proposed in the mid-nineties in,and with the purpose to facilitate the solution of problems involving complex geometries,free surfaces,moving boundaries and adaptive refinement. Since then,the FPM has evolved considerably,showing satisfactory accuracy and capabilities to deal with different fluid and solid mechanics problems.
Anders Szepessy is a Swedish mathematician.
Crystal plasticity is a mesoscale computational technique that takes into account crystallographic anisotropy in modelling the mechanical behaviour of polycrystalline materials. The technique has typically been used to study deformation through the process of slip,however,there are some flavors of crystal plasticity that can incorporate other deformation mechanisms like twinning and phase transformations. Crystal plasticity is used to obtain the relationship between stress and strain that also captures the underlying physics at the crystal level. Hence,it can be used to predict not just the stress-strain response of a material,but also the texture evolution,micromechanical field distributions,and regions of strain localisation. The two widely used formulations of crystal plasticity are the one based on the finite element method known as Crystal Plasticity Finite Element Method (CPFEM),which is developed based on the finite strain formulation for the mechanics,and a spectral formulation which is more computationally efficient due to the fast Fourier transform,but is based on the small strain formulation for the mechanics.
References
- ↑ "Executive Director". scii.chula.ac.th. Retrieved 2022-07-18.
- ↑ "Prof Worsak Kanok-Nukulchai is new AIT President - Asian Institute of Technology" . Retrieved 2022-07-18.
- ↑ "How engineering can adapt to the 'new normal'". Bangkok Post. Retrieved 2022-07-18.
- ↑ "Something for everyone". Bangkok Post. Retrieved 2022-07-18.
- ↑ "Taking the fight to Covid-19 using simple mathematics". Bangkok Post. Retrieved 2022-07-18.
- ↑ Hughes, Thomas J. R.; Taylor, Robert L.; Kanoknukulchai, Worsak (1977). "A simple and efficient finite element for plate bending". International Journal for Numerical Methods in Engineering. 11 (10): 1529–1543. doi:10.1002/nme.1620111005. ISSN 0029-5981.
- ↑ Hughes, Thomas J. R.; Taylor, Robert L.; Sackman, Jerome L.; Curnier, Alain; Kanoknukulchai, Worsak (1976-07-01). "A finite element method for a class of contact-impact problems". Computer Methods in Applied Mechanics and Engineering. 8 (3): 249–276. doi:10.1016/0045-7825(76)90018-9. ISSN 0045-7825.