Professor Thanh Tran

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 Nature, 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 Nature, 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 Nature, 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 Nature, 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 Nature, 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 Nature, 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 Nature, 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 Nature, 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 Nature, 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 Nature, 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 Nature, 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 Nature, 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 Nature, 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 Nature, 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 Nature, 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 | 2024

Vinod N; Tran T, 2024, 'Well-posedness and finite element approximation for the Landau–Lifshitz–Gilbert equation with spin torques', Applicable Analysis, http://dx.doi.org/10.1080/00036811.2024.2437787

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, 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 | 2016

Le Gia QT; Tran, T ; Nguyen HT, 2016, 'Solving the backward heat equation on the unit sphere', ANZIAM Journal : Electronic Supplement, pp. C262 - C278, http://journal.austms.org.au/ojs/index.php/ANZIAMJ/article/view/9346

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, 70, pp. 1401 - 1424, 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, 94, pp. 1051 - 1067, 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, 70, pp. 1970 - 1983, 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, 426, pp. 1232 - 1261, 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, 66, pp. 1389 - 1402, 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

Le Gia QT; Tran T, 2012, 'Fast iterative solvers for boundary value problems on a local spherical region', Proceedings of the 16th Computational Techniques and Applications Conference, published in ANZIAM Journal, 54, pp. C492 - C507, http://journal.austms.org.au/ojs/index.php/ANZIAMJ/article/view/6303/1730

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

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 Schwartz preconditioners for interpolation of divergence-free vector fields on spheres', The ANZIAM Journal, pp. C742 - C758

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

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

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

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

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

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, pp. 266 - 281

Journal articles | 2008

Le Gia QT; Tran T, 2008, 'Interpolation on the sphere: a fast solution technique', ANZIAM Journal, 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

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

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

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://www.sciencedirect.com/science/article/B6WPV-4F8K1JM-503/2/2886f934f125f4f4065f858d5968c2f9

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

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

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, 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, pp. 1243 - 1268

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, pp. 433 - 468

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, pp. 1901 - 1932

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, 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

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

Journal articles | 1998

Tran T; Stephan E; Zaprianov S, 1998, 'Wavelet-based preconditioners for boundary integral equations', Advances in Computational Mathematics, 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

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

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, pp. 1484 - 1493

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 | 2024

Goldys B; Soenjaya AL; Tran T, 2024, Global attractor and robust exponential attractors for some classes of fourth-order nonlinear evolution equations, http://dx.doi.org/10.48550/arxiv.2411.09034

Conference Papers | 2024

Nguyen C; Tran T; Le K; Nguyen H; Do T; Pham T; Luu ST; Vo T; Nguyen LM, 2024, 'Pushing the Boundaries of Legal Information Processing with Integration of Large Language Models', in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), pp. 167 - 182, http://dx.doi.org/10.1007/978-981-97-3076-6_12

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 | 2023

Soenjaya AL; Tran T, 2023, Stable $C^1$-conforming finite element methods for a class of nonlinear fourth-order evolution equations, http://dx.doi.org/10.48550/arxiv.2309.05530

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

Conference Papers | 2018

Nguyen D; Nguyen H; Nguyen A; Nguyen Y; Pham T; Koledov V; Kamantsev A; Mashirov A; Tran T; Kieu H; Yu S, 2018, 'Phase formation and magnetocaloric effect in (Pr,Nd)-Fe alloys prepared by rapidly quenched method', in EPJ Web of Conferences, http://dx.doi.org/10.1051/epjconf/201818505002

Conference Papers | 2018

Nguyen Y; Nguyen M; Vu Q; Pham T; Koledov V; Kamantsev A; Mashirov A; Tran T; Kieu H; Seong Y; Nguyen D, 2018, 'Investigation of magnetic phase transition and magnetocaloric effect of (Ni,Co)-Mn-Al melt-spun ribbons', in EPJ Web of Conferences, http://dx.doi.org/10.1051/epjconf/201818505001

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, presented at Domain Decomposition Methods in Science and Engineering XVII, St Wolfgang/Strobl, Austria, 03 July 2006 - 07 July 2006

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

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