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Professor Thanh Tran

Professor Thanh Tran

Professor
Science
School of Mathematics & Statistics

ABOUT ME

 

Biography

My research is situated in the broad field of computational mathematics. My current work focuses primarily on numerical methods for deterministic and stochastic partial differential equations.

Education

  • PhD, UNSW

 

RESEARCH

 

Research Goals

  • Create new mathematical theory and efficient numerical methods for solving problems in the physical sciences, engineering, and other fields.

Research in Detail

I have worked with integral equations, partial differential equations (both deterministic and stochastic). Apart from designing numerical methods and proving convergence, I have also designed techniques to accelerate the solution process, the so-called preconditioning techniques. Estimation of errors and adaptivity are other aspects of my research interests.

Research Grants

  • ARC Discovery Project 2022-2024: "Novel mathematics and efficient computational techniques for human vision", ($412K; 1st CI: J. Dick, 2nd CI: T. Tran, 3rd CI: Q.T. Le Gia)
  • ARC Discovery Project 2020-2022: "Mathematics for breaking limits of speed and density in magnetic memories" ($525K; 1st CI: B. Goldys, 2nd CI: T. Tran, 3rd CI: K-N Le)
  • ARC Discovery Project 2019-2021: "Novel mathematics and numerical methods for ferromagnetic problems" ($315K; 1st CI: T. Tran, 2nd CI: J. Dick)
  • ARC Discovery Project 2016-2018: "Novel approaches for problems with uncertainties" ($330K; 1st CI: T. Tran, 2nd CI: B. Goldys)
  • UNSW Goldstar Award 2015: "Novel approaches for problems with uncertainties".
  • ARC Discovery Project 2012-2014: "The mathematics of novel magnetic memory materials" ($330K; 1st CI: B. Goldys, 2nd CI: J.F. Grotowski, 3rd CI: T. Tran)
  • Go8-Germany Joint Research Co-operation Scheme 2013: "Shape calculus for interface problems" (German partner: A. Chernov)
  • UNSW Goldstar Award 2011: "Stochastic Landau-Lifchitz-Gilbert equation: From flows of harmonic maps to theory of novel magnetic materials" (co-CI, jointly with B. Goldys)

Current Student Projects (PhD and Honours)

Numerical methods for the Maxwell-Landau-Lifshitz-Gilbert equations.

Numerical methods for the stochastic Maxwell-Landau-Lifshitz-Gilbert equations.

Shape calculus for solving exterior boundary value problems.

Supervision Opportunities/Areas

If you are interested in any of the above topics, please write to me.

Advice for prospective students

The Computational Mathematics Group at UNSW is a vibrant group with extensive international collaborations and connections. If you are an enthusiastic student with strong mathematical talents and minimum skills in mathematical computing, you will find this group an attractive team to be with for a few years of your life.

 

TEACHING & OUTREACH

 

Courses I teach

MATH1251 (Mathematics for Actuarial Studies and Finance 1B - Calculus)

MATH3361/5361 (Stochastic Differential Equations: Theory, Applications, and Numerical Methods)

MATH3051 (Applied Real and Functional Analysis)

 

Professional affiliations and service positions

External Assessor, Universiti Putra Malaysia

 
Phone
+61 2 9385 7041
E-mail
thanh.tran@unsw.edu.au
Location
School of Mathematics and Statistics UNSW Sydney NSW 2052 The Red Centre Room 4061
  • Books | 2021
    Stephan EP; Tran T, 2021, Introduction, http://dx.doi.org/10.1007/978-3-030-79283-1_1
    Books | 2021
    Stephan EP; Tran T, 2021, Preface
    Books | 2021
    Stephan EP; Tran T, 2021, Schwarz Methods and Multilevel Preconditioners for Boundary Element Methods, http://dx.doi.org/10.1007/978-3-030-79283-1
  • Book Chapters | 2021
    Stephan EP; Tran T, 2021, 'A fully discrete method', in Schwarz Methods and Multilevel Preconditioners for Boundary Element Methods, Springer International Publishing, pp. 143 - 151, http://dx.doi.org/10.1007/978-3-030-79283-1_7
    Book Chapters | 2021
    Stephan EP; Tran T, 2021, 'Additive Schwarz methods for the hp-version', in Schwarz Methods and Multilevel Preconditioners for Boundary Element Methods, Springer International Publishing, pp. 127 - 141, http://dx.doi.org/10.1007/978-3-030-79283-1_6
    Book Chapters | 2021
    Stephan EP; Tran T, 2021, 'Diagonal scaling preconditioner and locally-refined meshes', in Schwarz Methods and Multilevel Preconditioners for Boundary Element Methods, Springer International Publishing, pp. 277 - 305, http://dx.doi.org/10.1007/978-3-030-79283-1_12
    Book Chapters | 2021
    Stephan EP; Tran T, 2021, 'FEM-BEM coupling', in Schwarz Methods and Multilevel Preconditioners for Boundary Element Methods, Springer International Publishing, pp. 331 - 366, http://dx.doi.org/10.1007/978-3-030-79283-1_14
    Book Chapters | 2021
    Stephan EP; Tran T, 2021, 'General framework of preconditioners', in Schwarz Methods and Multilevel Preconditioners for Boundary Element Methods, Springer International Publishing, pp. 13 - 69, http://dx.doi.org/10.1007/978-3-030-79283-1_2
    Book Chapters | 2021
    Stephan EP; Tran T, 2021, 'Implementation issues and numerical experiments', in Schwarz Methods and Multilevel Preconditioners for Boundary Element Methods, Springer International Publishing, pp. 175 - 202, http://dx.doi.org/10.1007/978-3-030-79283-1_9
    Book Chapters | 2021
    Stephan EP; Tran T, 2021, 'Indefinite problems', in Schwarz Methods and Multilevel Preconditioners for Boundary Element Methods, Springer International Publishing, pp. 153 - 174, http://dx.doi.org/10.1007/978-3-030-79283-1_8
    Book Chapters | 2021
    Stephan EP; Tran T, 2021, 'Introduction', in Schwarz Methods and Multilevel Preconditioners for Boundary Element Methods, Springer International Publishing, pp. 3 - 11, http://dx.doi.org/10.1007/978-3-030-79283-1_1
    Book Chapters | 2021
    Stephan EP; Tran T, 2021, 'Multilevel methods: The H-Version', in Schwarz Methods and Multilevel Preconditioners for Boundary Element Methods, Springer International Publishing, pp. 117 - 126, http://dx.doi.org/10.1007/978-3-030-79283-1_5
    Book Chapters | 2021
    Stephan EP; Tran T, 2021, 'Multilevel preconditioners with adaptive mesh refinements', in Schwarz Methods and Multilevel Preconditioners for Boundary Element Methods, Springer International Publishing, pp. 307 - 328, http://dx.doi.org/10.1007/978-3-030-79283-1_13
    Book Chapters | 2021
    Stephan EP; Tran T, 2021, 'Pseudo-differential equations with radial basis functions', in Schwarz Methods and Multilevel Preconditioners for Boundary Element Methods, Springer International Publishing, pp. 399 - 421, http://dx.doi.org/10.1007/978-3-030-79283-1_16
    Book Chapters | 2021
    Stephan EP; Tran T, 2021, 'Pseudo-differential equations with spherical splines', in Schwarz Methods and Multilevel Preconditioners for Boundary Element Methods, Springer International Publishing, pp. 369 - 398, http://dx.doi.org/10.1007/978-3-030-79283-1_15
    Book Chapters | 2021
    Stephan EP; Tran T, 2021, 'Two-level methods: The H-Version', in Schwarz Methods and Multilevel Preconditioners for Boundary Element Methods, Springer International Publishing, pp. 73 - 98, http://dx.doi.org/10.1007/978-3-030-79283-1_3
    Book Chapters | 2021
    Stephan EP; Tran T, 2021, 'Two-level methods: The P-version', in Schwarz Methods and Multilevel Preconditioners for Boundary Element Methods, Springer International Publishing, pp. 99 - 115, http://dx.doi.org/10.1007/978-3-030-79283-1_4
    Book Chapters | 2021
    Stephan EP; Tran T, 2021, 'Two-level methods: The hp-version on rectangular elements', in Schwarz Methods and Multilevel Preconditioners for Boundary Element Methods, Springer International Publishing, pp. 205 - 241, http://dx.doi.org/10.1007/978-3-030-79283-1_10
    Book Chapters | 2021
    Stephan EP; Tran T, 2021, 'Two-level methods: The hp-version on triangular elements', in Schwarz Methods and Multilevel Preconditioners for Boundary Element Methods, Springer International Publishing, pp. 243 - 276, http://dx.doi.org/10.1007/978-3-030-79283-1_11
    Book Chapters | 2018
    Tran T, 2018, 'Ian Sloan's legacy in integral equation methods', in Contemporary Computational Mathematics - A Celebration of the 80th Birthday of Ian Sloan, pp. 1127 - 1145, http://dx.doi.org/10.1007/978-3-319-72456-0_52
    Book Chapters | 2010
    Stephan EP; Tran T; Costea A, 2010, 'A boundary integral equation on the sphere for high-precision geodesy', in Kuczma M; Wilmanski K (ed.), Computer Methods in Mechanics, edn. 1, Springer-Verlag, Berlin and Heidelberg, pp. 99 - 110
    Book Chapters | 2008
    Maischak M; Stephan EP; Tran T, 2008, 'Domain decomposition algorithms for an indefinite hyper-singular integral equation in three dimensions', in Langer U; Discacciati M; Keyes DE; Widlund O; Zulehner W (ed.), Domain Decomposition Methods in Science and Engineering XVII, Springer, pp. 647 - 655
  • Journal articles | 2023
    Ahsan M; Tran T; Siraj-ul-Islam ; Hussain I, 2023, 'A multiresolution collocation method and its convergence for Burgers' type equations', Mathematical Methods in the Applied Sciences, 46, pp. 11702 - 11725, http://dx.doi.org/10.1002/mma.8764
    Journal articles | 2023
    Rufai MA; Tran T; Anastassi ZA, 2023, 'A variable step-size implementation of the hybrid Nyström method for integrating Hamiltonian and stiff differential systems', Computational and Applied Mathematics, 42, http://dx.doi.org/10.1007/s40314-023-02273-2
    Journal articles | 2023
    Soenjaya AL; Tran T, 2023, 'Global solutions of the Landau–Lifshitz–Baryakhtar equation', Journal of Differential Equations, 371, pp. 191 - 230, http://dx.doi.org/10.1016/j.jde.2023.06.033
    Journal articles | 2022
    An X; Majee AK; Prohl A; Tran T, 2022, 'Optimal control for a coupled spin-polarized current and magnetization system', Advances in Computational Mathematics, 48, http://dx.doi.org/10.1007/s10444-022-09947-1
    Journal articles | 2022
    Hausenblas E; Mukherjee D; Tran T, 2022, 'The one-dimensional stochastic Keller–Segel model with time-homogeneous spatial Wiener processes', Journal of Differential Equations, 310, pp. 506 - 554, http://dx.doi.org/10.1016/j.jde.2021.10.056
    Journal articles | 2021
    Tran T, 2021, 'Remarks on Sobolev norms of fractional orders', Journal of Mathematical Analysis and Applications, 498, pp. 124960 - 124960, http://dx.doi.org/10.1016/j.jmaa.2021.124960
    Journal articles | 2020
    Hausenblas E; Mukherjee D; Tran T, 2020, 'The one-dimensional stochastic Keller--Segel model with time-homogeneous spatial Wiener processes', , http://arxiv.org/abs/2009.13789v1
    Journal articles | 2020
    Mukherjee D; Tran T, 2020, 'A Shape calculus approach for time harmonic solid-fluid interaction problem in stochastic domains', , http://arxiv.org/abs/2009.13783v1
    Journal articles | 2020
    Pham DT; Tran T; Dinh D; Chernov A, 2020, 'Exterior Dirichlet and Neumann Problems in Domains with Random Boundaries', Bulletin of the Malaysian Mathematical Sciences Society, 43, pp. 1311 - 1342, http://dx.doi.org/10.1007/s40840-019-00741-9
    Journal articles | 2020
    Pham DT; Tran T, 2020, 'A parabolic equation on domains with random boundaries', , http://arxiv.org/abs/2009.13997v1
    Journal articles | 2020
    Shafie S; Tran T, 2020, 'Numerical studies: Adaptive mixed finite element schemes for Benjamin-bona-mahony and burgers equations', International Journal of Engineering Trends and Technology, pp. 63 - 69, http://dx.doi.org/10.14445/22315381/CATI1P211
    Journal articles | 2018
    Márquez A; Meddahi S; Tran T, 2018, 'Frequency-explicit asymptotic error estimates for a stress-pressure formulation of a time harmonic fluid-solid interaction problem', Computers and Mathematics with Applications, 76, pp. 2090 - 2109, http://dx.doi.org/10.1016/j.camwa.2018.08.006
    Journal articles | 2017
    Feischl M; Tran T, 2017, 'Existence of regular solutions of the landau-lifshitz-gilbert equation in 3d with natural boundary conditions', SIAM Journal on Mathematical Analysis, 49, pp. 4470 - 4490, http://dx.doi.org/10.1137/16M1103427
    Journal articles | 2017
    Feischl M; Tran T, 2017, 'The eddy current-LLG equations: Fem-Bem coupling and a priori error estimates', SIAM Journal on Numerical Analysis, 55, pp. 1786 - 1819, http://dx.doi.org/10.1137/16M1065161
    Journal articles | 2017
    Tuan NH; Khoa VA; Minh MN; Tran T, 2017, 'Reconstruction of the electric field of the Helmholtz equation in three dimensions', Journal of Computational and Applied Mathematics, 309, pp. 56 - 78, http://dx.doi.org/10.1016/j.cam.2016.05.021
    Journal articles | 2017
    Tuan NH; Long LD; Nguyen VT; Tran T, 2017, 'On a final value problem for the time-fractional diffusion equation with inhomogeneous source', Inverse Problems in Science and Engineering, 25, pp. 1367 - 1395, http://dx.doi.org/10.1080/17415977.2016.1259316
    Journal articles | 2016
    Feischl M; Tran T, 2016, 'The Eddy Current-LLG Equations-Part I: FEM-BEM Coupling', , http://arxiv.org/abs/1602.00744v1
    Journal articles | 2016
    Goldys B; Le KN; Tran T, 2016, 'A finite element approximation for the stochastic Landau-Lifshitz-Gilbert equation', Journal of Differential Equations, 260, pp. 937 - 970, http://dx.doi.org/10.1016/j.jde.2015.09.012
    Journal articles | 2015
    Chernov A; Pham D; Tran T, 2015, 'A shape calculus based method for a transmission problem with a random interface', Computers and Mathematics with Applications, http://dx.doi.org/10.1016/j.camwa.2015.06.021
    Journal articles | 2015
    Le KN; Page M; Praetorius D; Tran T, 2015, 'On a decoupled linear FEM integrator for eddy-current-LLG', Applicable Analysis, 94, pp. 1051 - 1067, http://dx.doi.org/10.1080/00036811.2014.916401
    Journal articles | 2015
    Márquez A; Meddahi S; Tran T, 2015, 'Analyses of mixed continuous and discontinuous galerkin methods for the time harmonic elasticity problem with reduced symmetry', SIAM Journal on Scientific Computing, 37, pp. A1909 - A1933, http://dx.doi.org/10.1137/14099022X
    Journal articles | 2015
    Nguyen VT; Nguyen HT; Tran TB; Vo AK, 2015, 'On an inverse problem in the parabolic equation arising from groundwater pollution problem', Boundary Value Problems, 2015, http://dx.doi.org/10.1186/s13661-015-0319-3
    Journal articles | 2015
    Pham DT; Tran T, 2015, 'Solving non-strongly elliptic pseudodifferential equations on a sphere using radial basis functions', Computers and Mathematics with Applications, 70, pp. 1970 - 1983, http://dx.doi.org/10.1016/j.camwa.2015.08.018
    Journal articles | 2015
    Tregubov I; Tran T, 2015, 'A Galerkin method with spherical splines for the shallow water equations on a sphere: error analysis', Numerische Mathematik, 129, pp. 783 - 814, http://dx.doi.org/10.1007/s00211-014-0654-9
    Journal articles | 2015
    Tuan NH; Thang LD; Khoa VA; Tran T, 2015, 'On an inverse boundary value problem of a nonlinear elliptic equation in three dimensions', Journal of Mathematical Analysis and Applications, 426, pp. 1232 - 1261, http://dx.doi.org/10.1016/j.jmaa.2014.12.047
    Journal articles | 2014
    Le K-N; Page M; Praetorius D; Tran T, 2014, 'On a decoupled linear FEM integrator for eddy-current-LLG', Applicable Analysis, http://dx.doi.org/10.1080/00036811.2014.916401
    Journal articles | 2014
    Márquez A; Meddahi S; Tran T, 2014, 'A mixed discontinuous Galerkin method for the time harmonic elasticity problem with reduced symmetry', , http://arxiv.org/abs/1410.1195v1
    Journal articles | 2014
    Pham DT; Tran T, 2014, 'Solving non-strongly elliptic pseudodifferential equations on a sphere using radial basis functions', Computers and Mathematics with Applications, http://dx.doi.org/10.1016/j.camwa.2015.08.018
    Journal articles | 2014
    Pham TD; Tran T, 2014, 'Strongly elliptic pseudodifferential equations on the sphere with radial basis functions', Numerische Mathematik, 128, pp. 589 - 614, http://dx.doi.org/10.1007/s00211-014-0614-4
    Journal articles | 2014
    Tregubov I; Tran T, 2014, 'A Galerkin method with spherical splines for the shallow water equations on a sphere: error analysis', Numerische Mathematik, http://dx.doi.org/10.1007/s00211-014-0654-9
    Journal articles | 2014
    Tuan NH; Thang LD; Khoa VA; Tran T, 2014, 'On an inverse boundary value problem of a nonlinear elliptic equation in three dimensions', Journal of Mathematical Analysis and Applications, http://dx.doi.org/10.1016/j.jmaa.2014.12.047
    Journal articles | 2013
    Heuer N; Tran T, 2013, 'A mixed method for Dirichlet problems with radial basis functions', Computers and Mathematics with Applications, 66, pp. 2045 - 2055, http://dx.doi.org/10.1016/j.camwa.2013.08.029
    Journal articles | 2013
    Le K-N; Tran T, 2013, 'A convergent finite element approximation for the quasi-static Maxwell-Landau-Lifshitz-Gilbert equations', Computers and Mathematics with Applications, http://dx.doi.org/10.1016/j.camwa.2013.08.009
    Journal articles | 2013
    Le K-N; Tran T, 2013, 'A finite element approximation for the quasi-static Maxwell--Landau--Lifshitz--Gilbert equations', ANZIAM Journal, 54, pp. 681 - 681, http://dx.doi.org/10.21914/anziamj.v54i0.6318
    Journal articles | 2013
    Le KN; Tran T, 2013, 'A convergent finite element approximation for the quasi-static Maxwell-Landau-Lifshitz-Gilbert equations', Computers and Mathematics with Applications, 66, pp. 1389 - 1402, http://dx.doi.org/10.1016/j.camwa.2013.08.009
    Journal articles | 2012
    Heuer N; Tran T, 2012, 'Radial basis functions for the solution of hypersingular operators on open surfaces', Computers and Mathematics With Applications, 63, pp. 1504 - 1518, http://dx.doi.org/10.1016/j.camwa.2012.03.038
    Journal articles | 2012
    Pham DH; Tran T; Crothers S, 2012, 'An overlapping additive Schwartz preconditioner for the Laplace-Beltrami equation using spherical splines', Advances in Computational Mathematics, 37, pp. 93 - 121, http://dx.doi.org/10.1007/s10444-011-9200-9
    Journal articles | 2012
    Pham DH; Tran T, 2012, 'A domain decomposition method for solving the hypersingular integral equation on the sphere with spherical splines', Numerische Mathematik, 120, pp. 117 - 151, http://dx.doi.org/10.1007/s00211-011-0404-1
    Journal articles | 2011
    Costea A; Le Gia Q; Stephan E; Tran T, 2011, 'Meshless BEM and overlapping Schwarz preconditioners for exterior problems on spheroids', Studia Geophysica et Geodaetica, 55, pp. 465 - 477, http://dx.doi.org/10.1007/s11200-011-0027-0
    Journal articles | 2011
    Le Gia QT; Stephan EP; Tran T, 2011, 'Solution to the Neumann problem exterior to a prolate spheroid by radial basis functions', Advances in Computational Mathematics, 34, pp. 83 - 103, http://dx.doi.org/10.1007/s10444-010-9145-4
    Journal articles | 2011
    Le Gia QT; Tran T, 2011, 'Additive Schwarz preconditioners for interpolation of divergence-free vector fields on spheres', ANZIAM Journal, 52, pp. C742 - C758
    Journal articles | 2011
    Pham T; Tran T; Chernov A, 2011, 'Pseudodifferential equations on the sphere with spherical splines', Mathematical Models and Methods in Applied Sciences, 21, pp. 1933 - 1959, http://dx.doi.org/10.1142/S021820251100560X
    Journal articles | 2011
    Shaik AR; Rahman SS; Tran NH; Tran T, 2011, 'Numerical simulation of fluid-rock coupling heat transfer in naturally fractured geothermal system', Applied Thermal Engineering, 31, pp. 1600 - 1606, http://dx.doi.org/10.1016/j.applthermaleng.2011.01.038
    Journal articles | 2011
    Shaik AR; Tran NH; Rahman SS; Tran T, 2011, 'Estimating Pressure Losses in Interconnected Fracture Systems: An Integrated Tensor Approach', International Journal of Geomechanics, 11, pp. 11pages, http://dx.doi.org/10.1061/(ASCE)GM.1943-5622.0000099
    Journal articles | 2010
    Le Gia QT; Tran T, 2010, 'An overlapping additive Schwarz preconditioner for interpolation on the unit sphere with spherical radial basis functions', Journal of Complexity, 26, pp. 552 - 573, http://dx.doi.org/10.1016/j.jco.2010.06.003
    Journal articles | 2010
    Tran T; Le Gia QT; Sloan IH; Stephan EP, 2010, 'Preconditioners for pseudodifferential equations on the sphere with radial basis functions', Numerische Mathematik, 115, pp. 141 - 163, http://dx.doi.org/10.1007/s00211-009-0269-8
    Journal articles | 2009
    Le Gia QT; Sloan IH; Tran T, 2009, 'Overlapping additive schwarz preconditioners for elliptic pdes on the unit sphere', Mathematics of Computation, 78, pp. 79 - 101, http://dx.doi.org/10.1090/S0025-5718-08-02150-9
    Journal articles | 2009
    Le Gia QT; Tran T; Sloan IH; Stephan EP, 2009, 'Boundary integral equations on the sphere with radial basis functions: error analysis', Applied Numerical Mathematics, 59, pp. 2857 - 2871, http://dx.doi.org/10.1016/j.apnum.2008.12.033
    Journal articles | 2009
    Tran T, 2009, 'Solutions to pseudodifferential equations using spherical radial basis functions', Bulletin of the Australian Mathematical Society, 79, pp. 473 - 485, http://dx.doi.org/10.1017/S0004972709000069
    Journal articles | 2008
    Le Gia QT; Pham TD; Tran T, 2008, 'Numerical solutions to a boundary integral equation with spherical radial basis functions', ANZIAM Journal, 50, pp. 266 - 281
    Journal articles | 2008
    Le Gia QT; Tran T, 2008, 'Interpolation on the sphere: a fast solution technique', ANZIAM Journal, 50, pp. 354 - 370
    Journal articles | 2008
    Tran T; Le Gia QT, 2008, 'Interpolation on the sphere: a fast solution technique', Australia and New Zealand Industrial and Applied Mathematics (ANZIAM) Journal, 50, pp. C354 - C370
    Journal articles | 2008
    Tran T, 2008, 'Meshless methods for pseudodifferential equations on the sphere', Oberwolfach Reports, No.19, pp. 10 - 12
    Journal articles | 2007
    Tran T, 2007, 'Additive Schwarz preconditioners for the h-p version boundary-element approximation to the hypersingular operator in three dimensions', International Journal of Computer Mathematics, 84, pp. 1417 - 1437, http://dx.doi.org/10.1080/00207160701293006
    Journal articles | 2005
    Teimoori Sangani A; Chen Z; Rahman SS; Tran T, 2005, 'Effective permeability calculation using boundary element method in naturally fractured reservoirs', Petroleum Science and Technology, 23, pp. 693 - 709, http://dx.doi.org/10.1081/LFT-200033029
    Journal articles | 2005
    Tran T; Duong T, 2005, 'A Posteriori error estimates with the finite element method of lines for a Sobolev equation', Numerical Methods for Partial Differential Equations, 21, pp. 521 - 535, http://dx.doi.org/10.1002/num.20045
    Journal articles | 2004
    Maischak M; Stephan EP; Tran T, 2004, 'A multiplicative Schwarz algorithm for the Galerkin boundary element approximation of the weakly singular integral operator in three dimensions', International Journal of Pure and Applied Mathematics, pp. 1 - 21
    Journal articles | 2004
    Tran T; Stephan E, 2004, 'An overlapping additive Schwarz preconditioner for boundary element approximations to the Laplace screen and Lame crack problems', Journal of Numerical Mathematics, 12, pp. 311 - 330, http://dx.doi.org/10.1163/1569395042571265
    Journal articles | 2004
    Tran T; Stephan EP, 2004, 'An overlapping additive Schwarz preconditioner for boundary element approximations to the Laplace screen and Lamé crack problems', Journal of Numerical Mathematics, 12, http://dx.doi.org/10.1515/1569395042571265
    Journal articles | 2003
    Teimoori A; Chen Z; Rahman SS; Tran T, 2003, 'Calculation of Permeability Tensor Using Boundary Element Method Provides a Unique Tool to Simulate Naturally Fractured Reservoirs', Proceedings - SPE Annual Technical Conference and Exhibition, pp. 5035 - 5042, http://dx.doi.org/10.2118/84545-ms
    Journal articles | 2002
    Tran T; Duong T, 2002, 'A complete analysis for some a posteriori error estimate with the ...', Numerical Functional Analysis and Optimization, 23, pp. 891 - 909, http://dx.doi.org/10.1081/NFA-120016275
    Journal articles | 2001
    Tran T; Stephan EP, 2001, 'Two-level additive Schwarz preconditioners for the h-p version of the Galerkin boundary element method for 2-d problems', Computing (Vienna/New York), 67, pp. 57 - 82, http://dx.doi.org/10.1007/s006070170016
    Journal articles | 2001
    Tran T, 2001, 'The tolerant qualocation method for variable-coefficient equations on curves', Journal of Integral Equations and Applications, 13, pp. 73 - 98, http://dx.doi.org/10.1216/jiea/996986883
    Journal articles | 2000
    Ainsworth M; Mclean W; Tran T, 2000, 'Diagonal scaling of stiffness matrices in the Galerkin boundary element method', Journal of Australian Mathematical Society B, 42, pp. 141 - 150
    Journal articles | 2000
    Kress R; Tran T, 2000, 'Inverse scattering for a locally perturbed half-plane', Inverse Problems, 16, pp. 1541 - 1559, http://dx.doi.org/10.1088/0266-5611/16/5/323
    Journal articles | 2000
    Stephan EP; Tran T, 2000, 'Domain decomposition algorithms for indefinite weakly singular integral equations: The h and p versions', IMA Journal of Numerical Analysis, 20, pp. 1 - 24, http://dx.doi.org/10.1093/imanum/20.1.1
    Journal articles | 2000
    Tran T; Maischak M; Stephan E, 2000, 'Multiplicative Schwarz algorithms for the Galerkin boundary element method', SIAM Journal on Numerical Analysis, 38, pp. 1243 - 1268, http://dx.doi.org/10.1137/S0036142997323983
    Journal articles | 2000
    Tran T; Stephan E, 2000, 'Additive Schwarz algorithms for the p version of the Galerkin boundary element method', American Journal of Science, 85, pp. 433 - 468, http://dx.doi.org/10.1007/s002110000125
    Journal articles | 2000
    Tran T, 2000, 'Overlapping additive Schwarz methods for first kind boundary integral equations', Journal of Integral Equations & Applications, 12, pp. 177 - 207
    Journal articles | 2000
    Tran T, 2000, 'Overlapping additive Schwarz preconditioners for boundary element methods', Journal of Integral Equations and Applications, 12, pp. 177 - 208, http://dx.doi.org/10.1216/jiea/1020282169
    Journal articles | 1999
    Ainsworth M; Mclean W; Tran T, 1999, 'The conditioning of boundary element equations on locally refined meshes and preconditioning by diagonal scaling', SIAM Journal on Numerical Analysis, 36, pp. 1901 - 1932, http://dx.doi.org/10.1137/S0036142997330809
    Journal articles | 1998
    Heuer N; Stephan E; Tran T, 1998, 'Multilevel additive Schwarz method for the h-p version of the Galerkin boundary element method', Mathematics of Computation, 67, pp. 501 - 518
    Journal articles | 1998
    Stephan E; Tran T, 1998, 'Domain decomposition algorithms for indefinite hypersingular integral equations: The h and p versions', SIAM journal of scientific computation, 19, pp. 1139 - 1153, http://dx.doi.org/10.1137/S1064827595296161
    Journal articles | 1998
    Tran T; Sloan IH, 1998, 'Tolerant Qualocation A Qualocation Method for Boundary Integral Equations with Reduced Regularity Requirement', Journal of Integral Equations and Applications, 10, pp. 85 - 115, http://dx.doi.org/10.1216/jiea/1181074209
    Journal articles | 1998
    Tran T; Stephan E; Zaprianov S, 1998, 'Wavelet-based preconditioners for boundary integral equations', Advances in Computational Mathematics, 9, pp. 233 - 249
    Journal articles | 1997
    Mclean W; Tran T, 1997, 'A preconditioning strategy of boundary element Galerkin methods', Numerical Methods for Partial Differential Equations, 13, pp. 283 - 301, http://dx.doi.org/10.1002/(SICI)1098-2426(199705)13:3<283::AID-NUM4>3.0.CO;2-J
    Journal articles | 1997
    Tran T; Stephan EP; Mund P, 1997, 'Hierarchical basis preconditioners for first kind integral equations', Applicable Analysis, 65, pp. 353 - 372, http://dx.doi.org/10.1080/00036819708840566
    Journal articles | 1996
    Matthias M; Stephen EP; Thanh T, 1996, 'Domain decomposition methods for boundary integral equations of the first kind: numerical results', Applicable Analysis, 63, pp. 111 - 132, http://dx.doi.org/10.1080/00036819608840498
    Journal articles | 1996
    Stephan EP; Tran T, 1996, 'Localization and Post Processing for the Galerkin Boundary Element Method Applied to Three-Dimensional Screen Problems', Journal of Integral Equations and Applications, 8, pp. 457 - 481, http://dx.doi.org/10.1216/jiea/1181075974
    Journal articles | 1996
    Tran T; Stephan E, 1996, 'Additive Schwarz methods for the h-version boundary element method', Applicable Analysis, pp. 63 - 84
    Journal articles | 1996
    Tran T, 1996, 'Locl error estimates for the Galerkin method applied to strongly elliptic integral equations on open curves', SIAM Journal on Numerical Analysis, 33, pp. 1484 - 1493, http://dx.doi.org/10.1137/S0036142993251401
    Journal articles | 1995
    Tran T, 1995, 'Domain decomposition methods for the Galerkin boundary element approximation applied to screen and crack problems', The Ho Chi Minh City Mathematical Society, 3, pp. 355 - 368
    Journal articles | 1995
    Tran T, 1995, 'The K-operator and the Galerkin method for strongly elliptic equations on smooth curves, local estimates', Mathematics of Computation, 64, pp. 501 - 513, http://dx.doi.org/10.2307/2153436
    Journal articles | 1995
    Tran T, 1995, 'The k-operator and the galerkin method for strongly elliptic equations on smooth curves: Local estimates1', Mathematics of Computation, 64, pp. 501 - 513, http://dx.doi.org/10.1090/S0025-5718-1995-1284671-2
    Journal articles | 1993
    Tran T, 1993, 'The K -Operator and the Qualocation Method for Strongly Elliptic Equations on Smooth Curves', Journal of Integral Equations and Applications, 5, pp. 299 - 243
    Journal articles | 1993
    Tran T, 1993, 'The K-operator and the qualocation method for strongly elliptic equations on smooth curves', Journal of Integral Equations and Applications, 5, pp. 405 - 428, http://dx.doi.org/10.1216/jiea/1181075762
    Journal articles | 1990
    ANG DD; THANH T, 1990, 'A NONLINEAR PSEUDOPARABOLIC EQUATION', PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 114, pp. 119 - 133, http://dx.doi.org/10.1017/S0308210500024306
  • Preprints | 2023
    Soenjaya AL; Tran T, 2023, Global solutions of the Landau--Lifshitz--Baryakhtar equation, , http://dx.doi.org/10.48550/arxiv.2302.02556
    Preprints | 2022
    Hausenblas E; Mukherjee D; Tran T, 2022, Uniqueness of the stochastic Keller-Segel model in one dimension, , http://dx.doi.org/10.48550/arxiv.2209.13188
    Preprints | 2017
    Goldys B; Le K-N; Tran T, 2017, A finite element approximation for the stochastic Maxwell--Landau--Lifshitz--Gilbert system, , http://dx.doi.org/10.48550/arxiv.1702.03027
    Conference Papers | 2017
    Shafie S; Tran T, 2017, 'A posteriori error estimation of H 1 mixed finite element method for the Benjamin-Bona-Mahony equation', in AIP Conference Proceedings, http://dx.doi.org/10.1063/1.4995921
    Preprints | 2016
    Feischl M; Tran T, 2016, The Eddy Current--LLG Equations: FEM-BEM Coupling and A Priori Error Estimates, , http://dx.doi.org/10.48550/arxiv.1602.00745
    Conference Papers | 2015
    Chernov A; Pham D; Tran T, 2015, 'A shape calculus based method for a transmission problem with a random interface Dedicated to E. Rank on the occasion of his 60th anniversary', in Computers and Mathematics with Applications, pp. 1401 - 1424, http://dx.doi.org/10.1016/j.camwa.2015.06.021
    Conference Papers | 2014
    Le Gia QT; Tran, T ; Nguyen HT, 2014, 'Solving the backward heat equation on the unit sphere', in ANZIAM Journal : Electronic Supplement, Australian Mathematical Society, ANU, pp. C262 - C278, presented at Computational Techniques and Applications Conference, ANU, 01 December 2014 - 03 December 2014, http://journal.austms.org.au/ojs/index.php/ANZIAMJ/article/view/9346
    Preprints | 2014
    Nguyen HT; Khoa VA; Minh MN; Tran T, 2014, Reconstruction of the electric field of the Helmholtz equation in 3D, , http://dx.doi.org/10.48550/arxiv.1408.1932
    Preprints | 2013
    Goldys B; Le K-N; Tran T, 2013, A finite element approximation for the stochastic Landau-Lifshitz-Gilbert equation, , http://dx.doi.org/10.48550/arxiv.1308.3912
    Preprints | 2013
    Le K-N; Page M; Praetorius D; Tran T, 2013, On a decoupled linear FEM integrator for Eddy-current-LLG, , http://dx.doi.org/10.48550/arxiv.1306.3319
    Conference Papers | 2012
    Le Gia QT; Tran T, 2012, 'Fast iterative solvers for boundary value problems on a local spherical region', in McCue S; Moroney T (ed.), Proceedings of the 16th Computational Techniques and Applications Conference, published in ANZIAM Journal, Australian Mathematical Society, Australia, pp. C492 - C507, presented at CTAC-2012, QUT, Brisbane, 23 September 2012 - 26 September 2012, http://journal.austms.org.au/ojs/index.php/ANZIAMJ/article/view/6303/1730
    Preprints | 2012
    Le K-N; Tran T, 2012, A convergent finite element approximation for the quasi-static Maxwell--Landau--Lifshitz--Gilbert equations, , http://dx.doi.org/10.48550/arxiv.1212.3369
    Conference Papers | 2012
    Tran T; Le KN, 2012, 'A finite element approximation for the quasi-static Maxwell--Landau--Lifshitz--Gilbert equations', in McCue S; Moroney T; Mallet D; Bunder J (eds.), Proceedings of the 16th Biennial Computational Techniques and Applications Conference, CTAC-2012, Australian Mathematical Society, Brisbane, QLD, pp. C681 - C698, presented at 16th Biennial Computational Techniques and Applications Conference, CTAC-2012, Brisbane, QLD, 23 September 2012 - 26 September 2012, http://dx.doi.org/10.0000/anziamj.v54i0.6318
    Conference Papers | 2012
    Tran T; Tregubov I, 2012, 'Efficient solvers for the Shallow Water Equations on a sphere', in McCue ; Moroney ; Mallet ; Bunder (eds.), CTAC2012 : Proceedings of the 16th Computational Techniques and Applications Conference, Australian Mathematical Society, Brisbane, QLD, pp. C412 - C428, presented at 16th Biennial Computational Techniques and Applications Conference, Brisbane, QLD, 23 September 2012 - 26 September 2012, http://journal.austms.org.au/ojs/index.php/ANZIAMJ/article/view/6836
    Conference Papers | 2010
    Le Gia QT; Tran T, 2010, 'Additive Schwartz preconditioners for interpolation of divergence-free vector fields on spheres', in The ANZIAM Journal, Australian Mathematical Society, Australia, pp. C742 - C758, presented at CTAC 2010, UNSW, Sydney, 28 November 2010 - 01 December 2010
    Conference Papers | 2010
    Stephan EP; Costea A; Le Gia QT; Tran T, 2010, 'Meshless boundary element methods for exterior problems on spheroids', in Advances in Boundary Element Techniques XI, EC Ltd, UK, London, pp. 455 - 461, presented at Boundary Element Techniques XI, Berlin, Germany, 12 July 2010 - 14 July 2010
    Conference Papers | 2008
    Tran T, 2008, 'Meshless methods for pseudodifferential equations on the sphere', in Oberwolfach Reports, Analysis of Boundary Element Methods, pp. 10 - 12, presented at Analysis of Boundary Element Methods, 13 April 2008 - 19 April 2008
    Conference Papers | 2006
    Stephan EP; Maischak M; Tran T, 2006, 'Domain decomposition algorithms for an indefinite hypersingular integral equation in three dimensions', in Domain Decomposition Methods in Science and Engineering XVII, St Wolfgang/Strobl, Austria, pp. 647 - 655, presented at Domain Decomposition Methods in Science and Engineering XVII, St Wolfgang/Strobl, Austria, 03 July 2006 - 07 July 2006, http://dx.doi.org/10.1007/978-3-540-75199-1_81
    Conference Papers | 2005
    Maichak M; Tran T, 2005, 'A block preconditioner for an electromagnetic FEM-BEM coupling problem is R3', in Wenbin L; Ng M; Shi Z (eds.), Proceeding of the 2nd International Conference on Scientific Computing and Partial Differential Equations, 02 December 2005 - 02 December 2005
    Conference Papers | 2005
    Maischak M; Tran T, 2005, 'A block preconditioner for an Electro-magnetic FE-BE coupling problem in R3', in 2nd International Conference on Scientific Computing and Partial Differential Equations, 2nd International Conference on Scientific Computing and Partial Differential Equations, Hong Kong Baptist University, presented at 2nd International Conference on Scientific Computing and Partial Differential Equations, Hong Kong Baptist University
    Conference Papers | 2003
    Teimoori Z; Chen Z; Rahman SS; Tran T, 2003, '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, Colorado, USA, 05 October 2003 - 08 October 2003, http://speonline.spe.org/
    Conference Papers | 1997
    Tran T, 1997, 'Additive Schwarz algorithms and the Galerkin boundary element method', in Noye J; Teubner M; Gill A (eds.), COMPUTATIONAL TECHNIQUES AND APPLICATIONS: CTAC 97, WORLD SCIENTIFIC PUBL CO PTE LTD, AUSTRALIA, ADELAIDE, pp. 703 - 710, presented at 8th Biennial Computational Techniques and Applications Conference (CTAC97), AUSTRALIA, ADELAIDE, 29 September 1997 - 01 October 1997, https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000077521700086&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1
    Theses / Dissertations | 1994
    Tran T, 1994, Localisation and Higher Order Averaging for Boundary Integral Equations., University of New South Wales