Welcome to my Homepage
Davoud Mirzaei
Associate Professor at Uppsala University
Department of Information Technology
Division of Scientific Computing
 Email: davoud.mirzaei@it.uu.se
 Phone: +46184712880
 Visiting Address: Room ÅNGESTRÖM 106180 hus 10, Lägerhyddsvägen 1
 Postal Address: BOX 337, 75105 UPPSALA
 Links:
Research
Research Interest
 Scattered data approximation methods
 Kernelbased methods
 Moving least squares approximation
 Numerical solution of PDEs
 Surface PDEs
 Highorder methods for hyperbolic PDEs
Short Research Presentation
My research foci are in developing, implementing, and analyzing the scattered data approximation methods for function approximation and numerical solution of partial differential equations. I am particularly interested in methods based on radial basis functions (RBFs) and moving least squares (MLS) approximations for numerical simulations on Euclidean spaces and on embedded submanifolds.
Academic Positions
Positions
Associate Professor, Uppsala University
2022  present
Associate Professor, University of Isfahan
2016  2022
Resident Reseacher, Institute for Research in Fundamental ScienceIPM
2017  2022
Nonresident Reseacher, Institute for Research in Fundamental ScienceIPM
2015  2017
Assistant Professor, University of Isfahan
2012  2016
Teaching
Books
Advanced Numerical Analysis (In Persian), Isfahan University Press, 2nd Ed. (2013)
Lecture notes

Computing, Error and Stability , Download PDF

Numerical Solution of Ordinary Differential Equations , Download PDF

Least Squares Problem, QR factorizarion and SVD , Download PDF

Stochastic Simulation and Monte Carlo Method , Download PDF

Elements of Numerical Analysis (In Persion, 243 pages) , Download PDF
Teaching experience
Uppsala University
Scientific Computing for Data Analysis (1TD352), Winter 2024
Scientific Computing for Data Analysis (1TD352), Fall 2023
Scientific Computing, Bridging Course (1TD045), Fall 2023
Scientific Computing II (1TD395), Spring 2023
Scientific Computing, Bridging Course (1TD045), Fall 2022
University of Isfahan
Numerical Solution of PDEs (FDM & FEM), 20112022
Theory and Application of Meshless Methods, 2014, 2016, 2018
Advanced Numerical Analysis, 20112022
Engineering Mathematics, 2019, 2020
Numerical Linear Algebra, 20132021
Elements of Numerical Analysis , 20132020
Approximation Theory, 2014
Special Topics in Numerical Analysis, 2013
Differential Equations 20132015, 2017
Numerical Analysis II, 2012
Numerical Analysis I, 2011
Amirkabir University of Technology
Numerical Analysis I, 2010
Differential Equations (TA), 2009
Calculus II (TA), 2008
Numerical Analysis I (TA), 2006, 2007
Publications
Journal papers
D. Mirzaei, N. Soodbakhsh, A nonoscillatory finite volume scheme using a weighted smoothed reconstruction, J. Comput. Phys. 508: 112981 (2024)
R. Mir, D. Mirzaei, The DRBFPU method for solving surface PDEs, J. Comput. Phys. 479: 112001 (2023)
D. Mirzaei, N. Soodbakhsh, A fault detection method based on partition of unity and kernel approximation, Numer. Algorithms, 93: 1759–1794, (2023).
S. Arefian, D. Mirzaei, A compact radial basis function partition of unity method, Comput. Math. Appl., 127: 111 (2022)
E. Farazandeh, D. Mirzaei, A rational RBF interpolation with conditionally positive kernels, Adv. Compu. Math., 47:74 (2021).
S. Seyednazari, M. Tatari, D. Mirzaei, Error and stability estimates of a leastsquares variational kernelbased method for second order elliptic PDEs, Comput. Math. Appl. 103 (2021) 111.
D. Mirzaei, The direct RBF partition of unity (DRBFPU) method for solving PDEs, SIAM Journal on Scientific Computing 43(1) (2021) A54A83.
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) 16821698.
M. Jabalameli, D. Mirzaei, A weakform RBF generated finite difference method, Computers and Mathematics with Applications, 79 (2020) 2624–2643.
D. Mirzaei, On analysis of kernel collocation methods for spherical PDEs, Applied Numerical Mathematics, 150 (2020) 222232.
V. Mohammadi, D. Mirzaei, M. Dehghan, Numerical simulation and error estimation of the timedependent AllenCahn equation on surfaces with radial basis functions, Journal of Scientific Computing, 79 (1) (2019) 493–516.
D. Mirzaei, A PetrovGalerkin kernel approximation on the sphere, SIAM J. Numer. Anal. 56 (1) (2018) 274 295.
D. Mirzaei, Direct approximation on spheres using generalized moving least squares, BIT Numerical Mathematics 27 (2017) 10411063.
K. Hasanpour, D. Mirzaei, A fast meshfree technique for coupled thermoelasticity problem, Acta Mechanica, 229 (2018) 2657 2673.
D. Mirzaei, A greedy meshless local PetrovGalerkin method based on radial basis functions, Numerical Methods for Partial Differential Equations, 32 (3) (2016) 847–861.
D. Mirzaei, K. Hasanpour, Direct meshless local Petrov–Galerkin method for elastodynamic analysis, Acta Mechanica, 227 (3) (2016) 619632.
D. Mirzaei, Error bounds for GMLS derivatives approximations of Sobolev functions, Journal of Computational and Applied Mathematics, 294 (2016) 93101
M. Ramezani, M. Mojtabaei, D. Mirzaei, DMLPG solution of the fractional advectiondiffusion problem, Engineering Analysis with Boundary Elements 59 (2015) 3642.
D. Mirzaei, Analysis of moving least squares approximation revisited, Journal of Computational and Applied Mathematics 282 (2015) 237250.
D. Mirzaei, A new lowcost meshfree method for two and three dimensional problems in elasticity, Applied Mathematical Modelling 39 (2015), 7181–7196
D. Mirzaei, R. Schaback, Solving heat conduction problems by the Direct Meshless Local PetrovGalerkin (DMLPG) method, Numerical Algorithms, 65 (2014) 275291.
D. Mirzaei, R. Schaback, Direct Meshless Local PetrovGalerkin (DMLPG) method: A generalized MLS approximation, Applied Numerical Mathematics, 68 (2013) 7382.
H. Hoseinzadeh, M. Dehghan, D. Mirzaei, The boundary element method for MagnetoHydrodynamic (MHD) channel flows at high Hartmann Numbers, Applied Mathematical Modelling, 37 (2013) 2337–2351.
D. Mirzaei, M. Dehghan, New implementation of MLBIE method for heat conduction problem in functionally graded materials, Engineering Analysis with Boundary Elements, 36 (2012) 511519.
D. Mirzaei, R. Schaback, M. Dehghan, On generalized moving least squares and diffuse derivatives, IMA Journal of Numerical Analysis, 32 (2012) 9831000.
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) 185210.
D. Mirzaei, M. Dehghan, MLPG approximation to the pLaplace problem, Computational Mechanics, 46 (2010) 805912 (with M. Dehghan)
D. Mirzaei, M. Dehghan, A meshless based method for solution of integral equations, Applied Numerical Mathematics, 60 (2010) 245262 (with M. Dehghan).
D. Mirzaei, M. Dehghan, Meshless local PetrovGalerkin approximation to the two dimensional SineGordon equation, Journal of Computational and Applied Mathematics, 233 (2010) 27372754.
D. Mirzaei, M. Dehghan, Implementation of meshless LBIE method to the 2D nonlinear SG problem, International Journal for Numerical Methods in Engineering, 79 (2009) 16621682.
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.
M. Dehghan, D. Mirzaei, A numerical method based on the boundary integral equation and dual reciprocity methods for one dimensional CahnHilliard equation, Engineering Analysis with Boundary Elements, 33 (2009) 522 528.
M. Dehghan, D. Mirzaei, Meshless Local PetrovGalerkin (MLPG) method for the unsteady magnetohydrodynamic (MHD) flow through pipe with arbitrary wall conductivity, Applied Numerical Mathematics, 59 (2009) 10431058.
D. Mirzaei, M. Dehghan, Boundary element solution of the twodimensional SineGordon equation using continuous linear elements, Engineering Analysis with Boundary Elements, 33 (2009) 1224.
M. Dehghan, D. Mirzaei, Numerical solution to the unsteady twodimensional Schrodinger equation using meshless local boundary integral equation method, International Journal for Numerical Methods in Engineering, 76 (2008) 501520.
M. Dehghan, D. Mirzaei, The boundary integral equation approach for numerical solution of the onedimensional SineGordon equation, Numerical Methods for Partial Differential Equations, 24 (2008) 14051425.
M. Dehghan, D. Mirzaei, The meshless local PetrovGalerkin (MLPG) method for the generalized twodimensional nonlinear Schrodinger equation, Engineering Analysis with Boundary Elements, 32 (2008) 747756.
M. Dehghan, D. Mirzaei, The dual reciprocity boundary element method (DRBEM) for twodimensional sineGordon equation, Computer Methods in Applied Mechanics and Engineering, 197 (2008) 476486.
Theses
Developments of MLSbased meshless methods, PhD Thesis, July 2011, Tehran. Download PDF

The fast multipole boundary element method for solving PDEs, Master Thesis, Jan. 2008, Tehran
Conference and Seminar Presentations (As speaker)

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

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

RBF Approximations for solving surface PDEs, TDBseminar, Division of Scientific Computing, University of Uppsala, Sweden, November 2022.

A Partition of Unity KernelBased Method for Surface PDEs, 2022 SIAM Annual Meeting (AN22), minisymposium on kernelbased approximation methods July 1115, 2022, Pennsylvania, US.

Rational RBF Interpolation, 10th Mathematics Conference of the Payamenoor University, May 1819, 2022, Shiraz.

A multivariate rational interpolation with conditionally positive definite kernels, 5th Dolomites Workshop on Constructive Approximation and Applications, September 610, 2021, Padova (Italy).

Scattered data approximation methods, an invited tutorial talk, 8th Seminar on Numerical Analysis and Its Applications, April 69, 2021.

A recent progress in localized RBF techniques, Keynote Speaker, 51st Annual Iranian Mathematics Conference, February 1619, 2021, Kashan, Iran.

The direct RBF partition of unity (DRBFPU) method, Invited talk in Online Workshop on RBFs: Theories, Applications and Recent Advances, 1619 June 2020, Hosted by Kharazmi University.

RBF Approximations on the Unit Sphere, Invited talk for IPMIsfahan Monthly Seminars, May 2020.

RBFFD in a weak formulation, Invited talk in the 3rd Caucasian Mathematics Conference, 2629 August 2019, RostovonDon, Russia.

On Scattered Data Approximation on the Unit Sphere, Invited talk in International Conference on Recent Achievements in Mathematical Science, 1418 Jan. 2019, Yazd.

Scattered Data Approximation by Kernels, Invited talk for IPMIsfahan Monthly Seminars, Dec 2017.

Direct approximation on spheres using generalized moving least squares, 4th Dolomites Workshop on Constructive Approximation and Applications, 813 September 2016, Albdi Canazei, Italy.

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

A direct approximation method with applications to engineering problems, International Conference on Learning and Approximation, 812 December 2014, Shanghai, China.

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

A numerical scheme based on boundary integral equation for onedimensional timedependent differential equations, The 40th Annual Iranian Mathematics Conference, Sharif Uni. of Tech. Tehran, 1388 (2009).
Other Activities
Editorial Board
Journal of the Iranian Mathematical Society (JIMS)
Bulletin of the Iranian Mathematical Society (BIMS) (Editor and Section Editor)
Computational Methods for Differential Equations (CMDE)
Iranian Journal of Numerical Analysis and Optimization (IJNAO)
Professional Experiences
Head of Department of Applied Mathematics & Computer Science, University of Isfahan, 20192021.
Head of Khansar's Faculty of Mathematics and Computer, 20172019.
Assistant Director of Research and Graduate Studies of Department of Mathematics, University of Isfahan, 20162017.
Collaboration in Conference Organizing
Member of the Scientific Committee of 10th Seminar on Numerical Analysis and Its Applications, Tabriz, 34 July, 2024, Iran.
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.
Member of the Scientific Committee of 9th Seminar on Numerical Analysis and Its Applications, Gulian, 911 May, 2022, Iran.
Member of the Scientific Committee of 8th Seminar on Numerical Analysis and Its Applications, Kurdistan, 69 April, 2021, Iran.
Member of the Scientific and Organizing Committees of 7th Conference on Frontiers in Mathematical Sciences, 13 January 2020, University of Isfahan & IPM.
Member of the Scientific Committee of 50th Annual Iranian Mathematics Conference, 2629 August 2019, Shiraz, Iran.
Member of the Scientific Committee of 4th International Conference on Natural Sciences (ICNS2019)Mathematics & Computer, 1819 April 2019, Sanandaj, Iran.
Organizer of the IPMIsfahan Workshop on Partial Differential Equations and Eigenvalue Problems, 1112 July, 2016, Isfahan, Iran.
Member of the Scientific Committee of 13th Seminar on Seminar on Differential Equations, Dynamical Systems and Applications, 1315 July 2016, Isfahan University of Technology, Iran.
Organizer of the IPMIsfahan Workshop on Numerical Analysis, 3031 May, 2015, Isfahan, Iran.
Member of the Scientific Committee of 5th Seminar on Numerical Analysis and Its Applications, Rafsanjan, 910 Sept. 2014, Iran.
Member of the Scientific and the Administrative Committees of 4th Seminar on Numerical Analysis and Its Applications, Khansar, 89 May 2013, Iran.
Copyright Davoud Mirzaei 2024