Welcome to my Homepage

Davoud Mirzaei

Associate Professor at Uppsala University

Department of Information Technology

Division of Scientific Computing

Contact Info

  • Email: davoud.mirzaei@it.uu.se
  • Phone: +4618-4712880
  • Visit: Room 106180, House 10, Ångeström
  • Postal Address: Box 337, 75105 UPPSALA

Links

Research

Research Interest

  • Scattered data approximation methods
  • Kernel-based methods
  • Moving least squares approximation
  • Numerical solution of PDEs
  • Surface PDEs
  • High-order methods for hyperbolic PDEs

Short Research Presentation

My research interests lie in developing, implementing, and analyzing numerical methods for function approximation and numerical solution of partial differential equations (PDEs). I have primarily focused on the scattered data approximation methods, which employ techniques based on unorganized points rather than predefined meshes. In this subject, I have followed and developed methods based on moving least squares (MLS) approximations and radial basis function (RBF) interpolations.

Academic Positions

Positions

Associate Professor, Uppsala University

2022 - present

 

Associate Professor, University of Isfahan

2016 - 2022

 

Resident Reseacher, Institute for Research in Fundamental Science-IPM

2017 - 2022

 

Non-resident Reseacher, Institute for Research in Fundamental Science-IPM

2015 - 2017

 

Assistant Professor, University of Isfahan

2012 - 2016

Open master thesis projects

Contact me if you are interested to do your master thesis (Spring 2025) on one of the following projects:

    1. MLS approximations for surface reconstruction from point cloud data, Download PDF

    2. RBF methods for solving conservation laws, Download PDF

    3. Numerical methods for simulating quantum skyrmions, Download PDF

Teaching

Books

    1. Advanced Numerical Analysis (In Persian), Isfahan University Press, 2nd Ed. (2013)

 

Lecture notes

    1. Fundamentals of Computing (50 pages) , Download PDF

    2. Numerical Solution of Ordinary Differential Equations (66 pages) , Download PDF

    3. Numerical Linear Algebra: Least Squares, QR and SVD (52 pages) , Download PDF

    4. Stochastic Simulation and Monte Carlo Method (87 pages) , Download PDF

    5. Elements of Numerical Analysis (In Persian, 243 pages) , Download PDF

 

Teaching experience

  • Uppsala University

    1. Scientific Computing for Data Analysis (1TD352), Fall 2023, Winter 2024, Fall 2024

    2. Scientific Computing, Bridging Course (1TD045), Fall 2022, Fall 2023, Fall 2024

    3. Scientific Computing II (1TD395), Spring 2023

  • University of Isfahan

    1. Advanced Numerical Analysis, 2011-2022 (master)

    2. Numerical Solution of PDEs (FDM & FEM) , 2011-2022 (master and PhD)

    3. Special Topics in Numerical PDEs, 2012, 2016, 2018, 2021 (PhD)

    4. Computational Methods in Data Mining, 2021 (master)

    5. Theory and Application of Meshless Methods, 2014, 2015, 2020 (PhD)

    6. Engineering Mathematics, 2016, 2020 (undergrad)

    7. Numerical Linear Algebra, 2013-2022 (undergrad)

    8. Elements of Numerical Analysis , 2013-2021 (undergrad)

    9. Approximation Theory, 2019 (PhD)

    10. Special Topics in Numerical Analysis, 2012 (master)

    11. Differential Equations 2012, 2014, 2017 (undergrad)

    12. Numerical Analysis II, 2011 (undergrad)

    13. Numerical Analysis I, 2011, 2012 (undegrad)

  • Amirkabir University of Technology

    1. Numerical Analysis I, 2009 (undegrad)

    2. Differential Equations (TA), 2008 (undegrad)

    3. Calculus II (TA), 2008 (undegrad)

    4. Numerical Analysis I (TA), 2006, 2007 (undegrad)

Publications

Journal papers

    1. D. Mirzaei, N. Soodbakhsh, A non-oscillatory finite volume scheme using a weighted smoothed reconstruction, J. Comput. Phys. 508: 112981 (2024). PDF

    2. R. Mir, D. Mirzaei, The D-RBF-PU method for solving surface PDEs, J. Comput. Phys. 479: 112001 (2023). PDF

    3. D. Mirzaei, N. Soodbakhsh, A fault detection method based on partition of unity and kernel approximation, Numer. Algorithms, 93: 1759–1794, (2023). PDF

    4. S. Arefian, D. Mirzaei, A compact radial basis function partition of unity method, Comput. Math. Appl., 127: 1-11 (2022). PDF

    5. E. Farazandeh, D. Mirzaei, A rational RBF interpolation with conditionally positive kernels, Adv. Compu. Math., 47:74 (2021). PDF

    6. S. Seyednazari, M. Tatari, D. Mirzaei, Error and stability estimates of a least-squares variational kernel-based method for second order elliptic PDEs, Comput. Math. Appl. 103 (2021) 1-11. PDF

    7. D. Mirzaei, The direct RBF partition of unity (D-RBF-PU) method for solving PDEs, SIAM Journal on Scientific Computing 43(1) (2021) A54-A83. PDF

    8. M. R. Ahmadi Darani, D. Mirzaei, A Petrov–Galerkin RBF method for diffusion equation on the unit sphere, Numerical Methods for Partial Differential Equations, 36 (2020) 1682-1698. PDF

    9. M. Jabalameli, D. Mirzaei, A weak-form RBF generated finite difference method, Computers and Mathematics with Applications, 79 (2020) 2624–2643. PDF

    10. D. Mirzaei, On analysis of kernel collocation methods for spherical PDEs, Applied Numerical Mathematics, 150 (2020) 222-232. PDF

    11. V. Mohammadi, D. Mirzaei, M. Dehghan, Numerical simulation and error estimation of the time-dependent Allen-Cahn equation on surfaces with radial basis functions, Journal of Scientific Computing, 79 (1) (2019) 493–516. PDF

    12. D. Mirzaei, A Petrov-Galerkin kernel approximation on the sphere, SIAM J. Numer. Anal. 56 (1) (2018) 274- 295. PDF

    13. D. Mirzaei, Direct approximation on spheres using generalized moving least squares, BIT Numerical Mathematics 27 (2017) 1041-1063. PDF

    14. K. Hasanpour, D. Mirzaei, A fast meshfree technique for coupled thermoelasticity problem, Acta Mechanica, 229 (2018) 2657- 2673.

    15. D. Mirzaei, A greedy meshless local Petrov-Galerkin method based on radial basis functions, Numerical Methods for Partial Differential Equations, 32 (3) (2016) 847–861.

    16. D. Mirzaei, K. Hasanpour, Direct meshless local Petrov–Galerkin method for elastodynamic analysis, Acta Mechanica, 227 (3) (2016) 619-632.

    17. D. Mirzaei, Error bounds for GMLS derivatives approximations of Sobolev functions, Journal of Computational and Applied Mathematics, 294 (2016) 93-101.

    18. M. Ramezani, M. Mojtabaei, D. Mirzaei, DMLPG solution of the fractional advection-diffusion problem, Engineering Analysis with Boundary Elements 59 (2015) 36-42.

    19. D. Mirzaei, Analysis of moving least squares approximation revisited, Journal of Computational and Applied Mathematics 282 (2015) 237-250. PDF

    20. D. Mirzaei, A new low-cost meshfree method for two and three dimensional problems in elasticity, Applied Mathematical Modelling 39 (2015), 7181–7196

    21. D. Mirzaei, R. Schaback, Solving heat conduction problems by the Direct Meshless Local Petrov-Galerkin (DMLPG) method, Numerical Algorithms, 65 (2014) 275-291. PDF

    22. D. Mirzaei, R. Schaback, Direct Meshless Local Petrov-Galerkin (DMLPG) method: A generalized MLS approximation, Applied Numerical Mathematics, 68 (2013) 73-82. PDF

    23. H. Hoseinzadeh, M. Dehghan, D. Mirzaei, The boundary element method for Magneto-Hydrodynamic (MHD) channel flows at high Hartmann Numbers, Applied Mathematical Modelling, 37 (2013) 2337–2351.

    24. D. Mirzaei, M. Dehghan, New implementation of MLBIE method for heat conduction problem in functionally graded materials, Engineering Analysis with Boundary Elements, 36 (2012) 511--519.

    25. D. Mirzaei, R. Schaback, M. Dehghan, On generalized moving least squares and diffuse derivatives, IMA Journal of Numerical Analysis, 32 (2012) 983-1000. PDF

    26. D. Mirzaei, M. Dehghan, MLPG method for transient heat conduction problem with MLS as trial approximation in both time and space domains, CMES: Computer Modeling in Engineering & Sciences, 72 (2011) 185-210.

    27. D. Mirzaei, M. Dehghan, MLPG approximation to the p-Laplace problem, Computational Mechanics, 46 (2010) 805-912 (with M. Dehghan)

    28. D. Mirzaei, M. Dehghan, A meshless based method for solution of integral equations, Applied Numerical Mathematics, 60 (2010) 245-262 (with M. Dehghan).

    29. D. Mirzaei, M. Dehghan, Meshless local Petrov-Galerkin approximation to the two dimensional Sine-Gordon equation, Journal of Computational and Applied Mathematics, 233 (2010) 2737-2754.

    30. D. Mirzaei, M. Dehghan, Implementation of meshless LBIE method to the 2D non-linear SG problem, International Journal for Numerical Methods in Engineering, 79 (2009) 1662-1682.

    31. M. Dehghan, D. Mirzaei, Meshless Local boundary integral equation (LBIE) method for the unsteady magnetohydrodynamic (MHD) flow in rectangular and circular pipes, Computer Physics Communications, 180 (2009) 1458- 1466.

    32. M. Dehghan, D. Mirzaei, A numerical method based on the boundary integral equation and dual reciprocity methods for one dimensional Cahn-Hilliard equation, Engineering Analysis with Boundary Elements, 33 (2009) 522- 528.

    33. M. Dehghan, D. Mirzaei, Meshless Local Petrov-Galerkin (MLPG) method for the unsteady magnetohydrodynamic (MHD) flow through pipe with arbitrary wall conductivity, Applied Numerical Mathematics, 59 (2009) 1043-1058.

    34. D. Mirzaei, M. Dehghan, Boundary element solution of the two-dimensional Sine-Gordon equation using continuous linear elements, Engineering Analysis with Boundary Elements, 33 (2009) 12-24.

    35. M. Dehghan, D. Mirzaei, Numerical solution to the unsteady two-dimensional Schrodinger equation using meshless local boundary integral equation method, International Journal for Numerical Methods in Engineering, 76 (2008) 501-520.

    36. M. Dehghan, D. Mirzaei, The boundary integral equation approach for numerical solution of the one-dimensional Sine-Gordon equation, Numerical Methods for Partial Differential Equations, 24 (2008) 1405-1425.

    37. M. Dehghan, D. Mirzaei, The meshless local Petrov-Galerkin (MLPG) method for the generalized two-dimensional non-linear Schrodinger equation, Engineering Analysis with Boundary Elements, 32 (2008) 747-756.

    38. M. Dehghan, D. Mirzaei, The dual reciprocity boundary element method (DRBEM) for two-dimensional sine-Gordon equation, Computer Methods in Applied Mechanics and Engineering, 197 (2008) 476-486.

Theses

    1. Developments of MLS-based meshless methods, PhD Thesis, July 2011, Tehran. Download PDF

    2. The fast multipole boundary element method for solving PDEs, Master Thesis, Jan. 2008, Tehran

Conference and Seminar Presentations (As speaker)

    1. A central RBF reconstruction for solving conservation laws, SwedComp 2024, October 23-24, 2024, KTH, Stockholm

    2. A CENO reconstruction using RBF approximations, 6th Dolomites Workshop on Constructive Approximation and Applications, 9-13 Sept. 2024, Canazei, Italy

    3. RBF techniques for reconstruction in FVM, 10th Seminar on Numerical Analysis and Its Applications, Invited speaker, 3-4 July, 2024, Tabriz

    4. An introduction to Monte Carlo method and the stochastic simulation algorithm (SSA), Three invited tutorial talks, March 3 - 5, 2024, Isfahan

    5. A high-order finite volume scheme using a weighted smoothed RBF reconstruction, SIAM Conference on Computational Science and Engineering (CSE23), February 26 - March 3, 2023, Amsterdam.

    6. RBF Approximations for solving surface PDEs, TDB-seminar, Division of Scientific Computing, University of Uppsala, Sweden, November 2022.

    7. A Partition of Unity Kernel-Based Method for Surface PDEs, 2022 SIAM Annual Meeting (AN22), minisymposium on kernel-based approximation methods July 11-15, 2022, Pennsylvania, US.

    8. Rational RBF Interpolation, 10th Mathematics Conference of the Payamenoor University, Invited speaker, May 18-19, 2022, Shiraz.

    9. A multivariate rational interpolation with conditionally positive definite kernels, 5th Dolomites Workshop on Constructive Approximation and Applications, September 6-10, 2021, Padova (Italy).

    10. Scattered data approximation methods, an invited tutorial talk, 8th Seminar on Numerical Analysis and Its Applications, April 6-9, 2021.

    11. A recent progress in localized RBF techniques, Keynote Speaker, 51st Annual Iranian Mathematics Conference, February 16-19, 2021, Kashan, Iran.

    12. The direct RBF partition of unity (D-RBF-PU) method, Invited talk in Online Workshop on RBFs: Theories, Applications and Recent Advances, 16-19 June 2020, Hosted by Kharazmi University.

    13. RBF Approximations on the Unit Sphere, Invited talk for IPM-Isfahan Monthly Seminars, May 2020.

    14. RBF-FD in a weak formulation, Invited talk in the 3rd Caucasian Mathematics Conference, 26-29 August 2019, Rostov-on-Don, Russia.

    15. On Scattered Data Approximation on the Unit Sphere, Invited talk in International Conference on Recent Achievements in Mathematical Science, 14-18 Jan. 2019, Yazd.

    16. Scattered Data Approximation by Kernels, Invited talk for IPM-Isfahan Monthly Seminars, Dec 2017.

    17. Direct approximation on spheres using generalized moving least squares, 4th Dolomites Workshop on Constructive Approximation and Applications, 8-13 September 2016, Albdi Canazei, Italy.

    18. Meshless Approximants, Invited talk in 6th Seminar on Numerical Analysis and its Applications, 19- 20 July 2016, Maragheh, Iran.

    19. A direct approximation method with applications to engineering problems, International Conference on Learning and Approximation, 8-12 December 2014, Shanghai, China.

    20. Recent developments in MLS based meshless methods, Invited talk in 4th Seminar on Numerical Analysis and Its Applications, Khansar, Iran, 1392 (2013).

    21. A numerical scheme based on boundary integral equation for one-dimensional time-dependent differential equations, The 40th Annual Iranian Mathematics Conference, Sharif Uni. of Tech. Tehran, 1388 (2009).

Other Activities

Editorial Board

    1. Journal of the Iranian Mathematical Society (JIMS)

    2. Bulletin of the Iranian Mathematical Society (BIMS) (Editor and Section Editor)

    3. Computational Methods for Differential Equations (CMDE)

    4. Iranian Journal of Numerical Analysis and Optimization (IJNAO)

 

Professional Experiences

    1. Head of Department of Applied Mathematics & Computer Science, University of Isfahan, 2019-2021.

    2. Head of Khansar's Faculty of Mathematics and Computer, 2017-2019.

    3. Assistant Director of Research and Graduate Studies of Department of Mathematics, University of Isfahan, 2016-2017.

 

Collaboration in Conference Organizing

    1. Member of the Scientific Committee of 10th Seminar on Numerical Analysis and Its Applications, Tabriz, 3-4 July, 2024, Iran.

    2. Member of Organizing Committee of the minisymposium ``Perspectives in Modern Kernel Approximation Methods" in SIAM Conference on Computational Science and Engineering (CSE23), February 26 - March 3, 2023, Amsterdam.

    3. Member of the Scientific Committee of 9th Seminar on Numerical Analysis and Its Applications, Gulian, 9-11 May, 2022, Iran.

    4. Member of the Scientific Committee of 8th Seminar on Numerical Analysis and Its Applications, Kurdistan, 6-9 April, 2021, Iran.

    5. Member of the Scientific and Organizing Committees of 7th Conference on Frontiers in Mathematical Sciences, 1-3 January 2020, University of Isfahan & IPM.

    6. Member of the Scientific Committee of 50th Annual Iranian Mathematics Conference, 26-29 August 2019, Shiraz, Iran.

    7. Member of the Scientific Committee of 4th International Conference on Natural Sciences (ICNS2019)-Mathematics & Computer, 18-19 April 2019, Sanandaj, Iran.

    8. Organizer of the IPM-Isfahan Workshop on Partial Differential Equations and Eigenvalue Problems, 11-12 July, 2016, Isfahan, Iran.

    9. Member of the Scientific Committee of 13th Seminar on Seminar on Differential Equations, Dynamical Systems and Applications, 13-15 July 2016, Isfahan University of Technology, Iran.

    10. Organizer of the IPM-Isfahan Workshop on Numerical Analysis, 30-31 May, 2015, Isfahan, Iran.

    11. Member of the Scientific Committee of 5th Seminar on Numerical Analysis and Its Applications, Rafsanjan, 9-10 Sept. 2014, Iran.

    12. Member of the Scientific and the Administrative Committees of 4th Seminar on Numerical Analysis and Its Applications, Khansar, 8-9 May 2013, Iran.

  Copyright Davoud Mirzaei 2024