American Journal of Computational and Applied Mathematics

American Journal of Computational and Applied Mathematics is a peer-reviewed international journal. This journal publishes significant research papers from all branches of applied mathematical and computational sciences. It publishes original papers of high scientific value in all areas of computational and applied mathematics.

Thanh Tran

Editorial Board Member of American Journal of Computational and Applied Mathematics

Associate Professor, University of New South Wales, Australia

Research Areas

Numerical Analysis, Computional Mathematics

Education

1994PhDMathematics, The University of New South Wales
1981BSc Hons Mathematics, The University of Ho Chi Minh City

Experience

2012Associate Professor, Director of Postgraduate Studies, School of Mathematics and Statistics, The University of New South Wales, Australia
2002-2011Senior Lecturer, Director of Postgraduate Studies, School of Mathematics and Statistics, The University of New South Wales, Australia
2001Lecturer, School of Computing and Mathematics, Deakin University, Australia
1997-2000Research Fellow, Centre for Mathematics and its Applications, School of Mathematical Sciences, Australian National University
1994-1997 Postdoctoral Research Associate, School of Mathematics, The University of New South Wales, Australia

Publications: Journals

[1]  D. Pham, T. Tran, A domain decomposition method for solving the hypersingular integral equation on the sphere with spherical splines, Numerische Mathematik DOI 10.1007/s00211-011-0404-1.
[2]  D. Pham, T. Tran, A. Chernov, Pseudodifferential equations on the sphere with spherical splines, Mathematical Models and Methods in Applied Science 21, (2011) 1933-1959.
[3]  D. Pham, T. Tran, S. Crothers, An overlapping additive Schwarz preconditioner for the Laplace-Beltrami equation using spherical splines, Advances in Computational Mathematics, DOI 10.1007/s10444-011-9200-9 (2011).
[4]  A. R. Shaik, N. H. Tran, S. S. Rahman, T. Tran, Numerical simulation of fluid-rock coupling heat transfer in naturally fractured geothermal system, Applied Thermal Engineering (to appear).
[5]  A. R. Shaik, N. H. Tran, S. S. Rahman, T. Tran, Estimating pressure losses in interconnected fracture systems: An integrated tensor approach, International Journal of Geomechanics, DOI:10.1061/(ASCE)GM.1943-5622.0000099 (2011).
[6]  Q.T. Le Gia, E.P. Stephan, T. Tran, Solution to the Neumann problem exterior to a prolate spheroid by radial basis functions, Advances in Computational Mathematics 34(1) (2011), 83-103.
[7]  T. Tran, Q.T. Le Gia, I.H. Sloan, E.P. Stephan, Preconditioners for pseudodifferential equations on the sphere with radial basis functions, Numerische Mathematik, 115(1) (2010), 141-163.
[8]  Q. T. Le Gia, T. Tran, An overlapping additive Schwarz preconditioner for interpolation on the unit sphere by spherical basis functions, Journal of Complexity, 26(5) (2010), 552-573.
[9]  T. Tran, Q. T. Le Gia, I. H. Sloan, and E. P. Stephan, Boundary integral equations on the sphere with radial basis functions: Error analysis, Applied Numerical Mathematics, 59 (2009), 2857-27871.
[10]  Q. T. Le Gia, I. H. Sloan, T. Tran, Overlapping additive Schwartz preconditioners for elliptic PDEs on the unit sphere, Mathematics of Computation, 78(1) (2009), 79-101.
[11]  T. D. Pham, T. Tran, Solutions to pseudodifferential equations using spherical radial basis functions, Bulletin of the Australian Mathematical Society, 79 (2009), 473-485.
[12]  T. Tran, Additive Schwarz preconditioners for the h-p version boundary element approximation to the hypersingular operator in three dimensions, International Journal of Computer Mathematics, 84 (2007), 1417-1437.
[13]  T. Tran and T.B. Duong, A posteriori error estimates with the finite element method of lines for a Sobolev equation, Numer. Meth. PDE 21 (2005), 521-535.
[14]  A. Teimoori, Z. Chen, S.S. Rahman and T. Tran, Effective permeability calculation using boundary element method in naturally fractured reservoirs, Petroleum Science and Technology, 23 (2005), 693-709.
[15]  M. Maischak, E. P. Stephan and T. Tran, A Multiplicative Schwarz Algorithm for the Galerkin Boundary Element Approximation of the Weakly Singular Integral Operator in Three Dimensions, Int. J. Pure & Appl. Maths. 12 (2004), 1-21.
[16]  T. Tran, E. P. Stephan, An overlapping additive Schwarz preconditioner for boundary element approximations to the Laplace screen and Lam´e crack problems, J. Numer. Math., 12 (2004), 311-330.
[17]  T. Tran and T.B. Duong, A Complete Analysis for Some A Posteriori Error Estimates with the Finite Element Method of Lines for a Nonlinear Parabolic Equation, J. Numer. Funct. Anal. Optim. 23 (2002), 891-909.
[18]  T. Tran and E.P. Stephan, Two-level Additive Schwarz Preconditioners for the h-p Version of the Galerkin Boundary Element Method, Computing 67 (2001), 57-82.
[19]  I.H. Sloan and T. Tran, A Tolerant Qualocation Method for Variable-Coefficient Elliptic Equations on Curves, Journal of Integral Equations & Applications 13 (2001), 73-98.
[20]  M. Maischak, E. P. Stephan and T. Tran, Multiplicative Schwarz Algorithms for the Galerkin Boundary Element Method, SIAM Journal on Numerical Analysis 38 (2000), 1243-1268.
[21]  R. Kress and T. Tran, Inverse Scattering for a Locally Perturbed Half-Plane, Inverse Problems 16 (2000), 1541-1559.
[22]  T. Tran, Overlapping Additive Schwarz Methods for First Kind Boundary Integral Equations, Journal of Integral Equations & Applications 12 (2000), 177-207.
[23]  T. Tran and E.P. Stephan, Additive Schwarz Algorithms for the p Version of the Galerkin Boundary Element Method, Numerische Mathematik 85 (2000), 433-468.
[24]  E. P. Stephan and T. Tran, Domain Decomposition Algorithms for Indefinite Weakly Singular Integral Equations: the h and p Versions, IMA Journal of Numerical Analysis 20 (2000), 1-24.
[25]  M. Ainsworth, W. McLean, and T. Tran, Diagonal Scaling of Stiffness Matrices in the Galerkin Boundary Element Method, ANZIAM J. 42 (2000), 141-150.
[26]  M. Ainsworth, W. McLean, and T. Tran, The Conditioning of Boundary Element Equations on Locally Refined Meshes and Preconditioning by Diagonal Scaling, SIAM Journal on Numerical Analysis 36 (1999), 1901-1932.
[27]  T. Tran, E. P. Stephan and S. Zaprianov, Wavelet-Based Preconditioners for Boundary Integral Equations, Advances in ComputationalMathematics 9 (1998), 233-249.
[28]  T. Tran and I. H. Sloan, Tolerant Qualocation-A Qualocation Method for Boundary Integral Equations with Reduced Regularity Requirement, Journal of Integral Equations & Applications 10 (1998), 85-115.
[29]  E. P. Stephan and T. Tran, Domain Decomposition Algorithms for Indefinite Hypersingular Integral Equations: the h and p Versions, SIAM Journal of Scientific Computing 19 (1998), 1139-1153.
[30]  N. Heuer, E. P. Stephan and T. Tran, A Multilevel Additive Schwarz Method for the h-p Version of the Galerkin Boundary Element Method, Mathematics of Computation 67 (1998), 501-518.
[31]  T. Tran, E.P. Stephan, and P. Mund, Hierarchical Basis Preconditioners for First Kind Integral Equations, Applicable Analysis 65 (1997), 353-372.
[32]  W. McLean and T. Tran, A Preconditioning Strategy for Boundary Element Galerkin Methods, Numerical Methods for PDE's 13 (1997), 283-301.
[33]  M. Maischak, E. P. Stephan and T. Tran, Domain Decomposition for Integral Equations of the First Kind: Numerical Results, Applicable Analysis 63 (1996), 111-132.
[34]  T. Tran and E. P. Stephan, Additive Schwarz Methods for the h Version Boundary Element Method, Applicable Analysis 60 (1996), 63-84.
[35]  T. Tran, Local Error Estimates for the Galerkin Method Applied to Strongly Elliptic Integral Equations on Open Curves, SIAM Journal on Numerical Analysis 33 (1996), 1484-1493.
[36]  E. P. Stephan and T. Tran, Localisation and Post Processing for the Galerkin Boundary Element Method Applied to Three-Dimensional Screen Problems, Journal of Integral Equations & Applications 8 (1996), 457-481.
[37]  T. Tran, The K-Operator and the Galerkin Method for Strongly Elliptic Equations on Smooth Curves: Local Estimates, Mathematics of Computation 64 (1995), 501-513.
[38]  T. Tran, The K-Operator and the Qualocation Method for Strongly Elliptic Equations on Smooth Curves, Journal of Integral Equations & Applications 5 (1993), 405-428.
[39]  D. D. Ang and T. Tran, A Nonlinear Pseudoparabolic Equation, Proceedings of the Royal Society of Edinburgh 114A (1990), 119-133.

Publications: Conferences/Workshops/Symposiums

[1]  T. Tran, Meshless methods for pseudodifferential equations on the sphere, in: Oberwolfach Report No. 19, (2008), 10-12.
[2]  T. D. Pham, T. Tran and Q. T. Le Gia, Numerical solutions to a boundaryintergral equation with spherical radial basis functions, Proceedings of the 14th Biennial Computational Techniques and Applications Conference, CTAC-2008, volume 50 of ANZIAM J., pages C266-C281, Nov. 2008.
[3]  T. Tran, Q. T. Le Gia, Interpolation on the sphere: a fast solution technique, Proceedings of the 14th Biennial Computational Techniques and Applications Conference, CTAC-2008, volume 50 of ANZIAM J., pages C354-C370, Nov. 2008.
[4]  M. Maischak, E. P. Stephan, T. Tran, Domain decomposition algorithms for an indefinite hypersingular integral equation in three dimensions, in: Domain Decompostion Methods in Science and Engineering XVII, Springer, (2008), 647-655.
[5]  T. Tran, A preconditioner for the boundary-element approximation of the Helmholtz equation in R3, Proceedings of the International Conference on Nonlinear Analysis & Engineering Mechanics Today (2007), 604-613.
[6]  M. Maichak, T. Tran, A block preconditioner for an electromagnetic FEM-BEM coupling problem is R3, Proceedings of the 2nd International Conference on Scientific Computing and Partial Differential Equations, (2007), 302-318.
[7]  A. Teimoori, Z. Chen, S. S. Rahman, T. Tran, Calculation of permeability tensor using boundary elements method provides a unique tool to simulate naturally fractured reservoirs, in: Proceedings of the SPE Annual Technical Conference and Exhibition, Colorado, USA. 5-8 October, 2003, (2003), http://speonline.spe.org.
[8]  T. Tran, Additive Schwarz Preconditioners for a Fully-Discrete and Symmetric Boundary Element Method, Computational Techniques and Applications: CTAC99, ANZIAM Journal 42(E), 2000, pp C1420-1442.
[9]  T. Tran, Additive Schwarz Algorithms and the Galerkin Boundary Element Method, Computational Techniques and Applications: CTAC97, eds: J. Noye, M. Teubner, and A. Gill, World Scientific, Singapore, 1998, pp 703-710.
[10]  M. Maischak, E.P. Stephan and T. Tran, Two Level Schwarz Methods for Indefinite Integral Equations, Proceedings of the 9th Conference on Domain Decomposition Methods, 1996, eds: P. Bjørstad, M. Espedal and D. Keyes. Electronic Proceedings: http://www.DDM.org/DD9, c 1998 DDM.org, pp 504-508.
[11]  T. Tran, Domain Decomposition Methods for the Galerkin Boundary Element Approximation Applied to Screen and Crack Problems, Analysis and Mechanics of Continuous Media (Proceedings of an International Conference in honour of D.D. Ang, Ho Chi Minh City, 27-29 December 1995) (eds: N.H. Anh, D.M. Duc, B.D. Khanh, P.Q. Khanh, and T.D. Van), The Ho Chi Minh City Mathematical Society, Vol. 3, 1995, pp 355-368.

Publications: Books/Book Chapters

[1]  D. Harrar II and T. Tran, Proceedings of the 9th Biennial Computational Techniques and Applications Conference and Workshops, ANZIAM Journal 42 (E), 2000 (http://anziamj.austms.org.au/V42/CTAC99).
[2]  T. Tran, Localisation and Higher Order Averaging for Boundary Integral Equations, PhD Thesis, University of New South Wales, 1994.
[3]  E. P. Stephan, T. Tran, A. Costea, A boundary integral equation on the sphere for high-precision geodesy, pages 99-110, Chapter 6 of Computer Methods in Mechanics, Lectures of the CMM2009. Edited by M. Kuczma and K. Wilmanski, 2010, Springer-Verlag, Berlin Heidelberg.