Dr.rer.nat. M.K.Abeyratne

B.Sc. (Kelaniya, Sri Lanka)

Diploma (J'Pura, Sri Lanka)

M.Sc.nat. (K'lautern, Germany)

Dr.rer.nat. (K'lautern, Germany)


Cinque Terre
Department of Mathematics
Faculty of Science
University of Ruhuna
Matara 81000, SRI LANKA
E-mail abeyratn@maths.ruh.ac.lk

Numerical Methods for partial differential equations, Industrial Mathematics, Mathematical Modelling, Spherical Harmonics, Wavelets and Multiscale Analysis, Elliptic boundary value problems in elasticity, Geo-scientific applications, Computational Methods in Seismic Tomography.
Mathematical Analysis, Applied Functional Analysis, Scientific Computing, Mathematical Modeling, Numerical Methods for ODEs and PDE's, Systems and Control Theory, Nonparametric Kernel Smoothing Techniques,Mathematics (Foundation courses for other disciplines such as Engineering, Economics etc).
Mathematical Modelling, M.Sc. in Industrial Mathematics, University of Sri Jayewardenepura, Sri Lanka

(2015/16) Exploration of Geothermal Sources in Sri Lanka combining Computational Methods through Seismic Wave Modelling, Magneto-Telluric Techniques and other Geophysical Experiments (Co-investigators M.K.Abeyrtane and Prof. P.A. Jayantha (University of Ruhuna), Dr. N.D. Subasinghe (IFS, Kandy), Dr. Shantha Gamage (University of Sri Jayewardenepura) (Proposal is submitted to the Ministry of Defense, Sri Lanka for approval and support) .

(2016) Wavelet based computational Method for solving Reaction-Diffusion Models with Dirichlet and Neumann Boundary Conditions, and their Applications in Biology, (ongoing in collaboration with Prof. D.Patel , (University of Baroda, India))

(2016) Construction of Wavelet based Multiresolution Techniques coupling with Finite Volume Method for solving Partial Differential Equations. A collaborative work with Prof. P.A. Jayantha (University of Ruhuna), Prof. D.Patel , (University of Baroda, India) (Proposed and to be started)

(2013/14) A Study on Wavelet Galerkin Approximation for Elliptic Boundary Value Problems arising in Electro Magnetic Theory This is a joint research project in collaboration with Center for Industrial Mathematics Faculty of Engineering, The M.S. University of Baroda, Gujarat, India (partially completed and two papers were published).

(2013) Multiscale modeling in seismic tomography: A Collaborative research project with Geomathematics Group, TU Kaiserslautern, Germany. This is mainly a wavelet based computational method in solving elastic wave equation. Based on recent result of acoustic wave scattering, the new research pathways are initiated tonsorial wavelet based multiscale method in the analysis of scattered elastic wave fields within seismic tomography (contributed).

(2012/13) A collaborative research project between the Department of Mathematics, University of Ruhuna and National Institute of Technology, Calicut, Kerala, India on the topic of Surface temperature reconstruction from free surface data in thin film on a stretching sheet - Project is granted by India Sri Lanka Foundation(ISLF) (Completed and published a paper in an international journal in 2014)

(2010) Faculty of Science, University of Ruhuna Project Title: Determination of regional gravity anomaly and a study of a topographic density variation over the geoid in the region of Sri Lanka using a multiresolution technique based on scalar spherical wavelets with satellite observations (Completed as an undergraduate research project)

2015 Resource person (Academic/International), Indo-European Study Group Meeting on Industrial Problems - IESGMIP2015 held at the Faculty of Engineering and Technology, MS University of Baroda, India 3-11 January 2015.

2014 Secretary/Convener and a resource person, Study Group Meeting on Mathematics and Statistics - SGMMSI-2014 Organized by the Department of Mathematics, University of Ruhuna in collaboration with ITRCC, University of Ruhuna - December 2-5, 2014.

2013 March Resource Person and organizer One-Day workshop on Mathematics In industry, University of Ruhuna, Sri Lanka, organized in collaboration with M.S. University, Baroda India.

2013 March Invited Research Fellow : Department of Mathematics, National Institute of Technology, Calicut, India. Delivered a lecture on "Geomathematics : Case Studies on Mathematical Modeling in Geoscience", Collaborative research project funded by ISLF.

2012 December Resource Person Indo-European Modeling week and Study Group Meeting on Industrial Mathematics, The Maharaja Sayajirao University of Baroda, Gujarat, India.

2011 March Invited Delegate International Conference on "Mathematical Modelling and Applications to Industrial Problems (MMIP2011)", NIT Calicut, Kerala, India.

2009 March, Resource Person, Mathematics in Industry, Medicine Commerce and Plant Sciences Study Group Meeting (MIMCPSSGM-09)24-28 March 2009 The Maharaja Sayajirao University of Baroda, Gujarat, INDIA.

2007 January, Invited speaker, International conference on current trends in industrial and applied mathematics January 16-18, 2007, Department of Applied Mathematics, Faculty of Technology and Engineering, The M.S. University of Baroda, Gujarat, India

2006 September Participant International Conference on Applied Mathematics on "There is nothing more practical than a good theory" Sep 14-15, 2006, Fraunhofer Institute of Technoundwirschaftsmathematik, Kaiserslautern, Germany, (http://www.itwm.fraunhofer.de)

2005 December Participant Training programme on Remote Sensing and GIS for Coastal Zone Management for Disaster Mitigation organized by Geoinfomatic Center, AIT Thailand, Japanese Aerospace Exploration Agency (JAXA) and Department of Surveys, Sri Lanka.

2005 December Contributed talk Annual Conference on Earth System Processes related to Earthquakes, tsunamis and Volcanic Eruptions organized by Indian Geophysical Union and Barkatullah University, Bhopal,India.

2004 Invited Delegate Conference in Modelling and Simulation in Life Sciences, Materials and Technology, in honour of Prof. Dr..Dr. Helmut Neunzert, Germany. Doyen of Industrial Mathematics, (December 7-10, 2004), Indian Institute of Technology, Madras, India. (Participated as an invited delegate and as a resource person to deliver a felicitation talk).

M.K.Abeyratne, W.J. Jannidi (2016), A Comparative Simulation Study on Estimation of Density Functions for Finite Mixtures and Data Clustering using Nonparametric Kernel Smoothing with EM Algorithm, International Conference on Applications of Mathematics for Nonlinear sciences (ANMS) 2016, Kathmandu, Nepal, May 26-29, 2016).

M.P.A. Wijayasiri and M.K.Abeyratne, (2015) An Application of Nonparametric Kernel Density Estimators in Colombo Stock Market Indices, Proceedings of 2nd Ruhuna International Science & Technology Conference (RISTCON2015), January 22-23, 2015, Faculty of Science, University of Ruhuna, Matara, Sri Lanka Page 68.

Pasdunkorale A. Jayantha and M.K.Abeyratne, (2015) A Study on Parameter estimation in modelling using a model independent program-PEST, Proceedings of 2nd Ruhuna International Science & Technology Conference (RISTCON2015),January 22-23, 2015, Faculty of Science, University of Ruhuna, Matara, Sri Lanka Page 78.

S. Panda, Mathieu Sellier, M. C. S. Fernando, and M. K. Abeyratne, Process Parameter Identification in Thin Film Flows Driven by a Stretching Surface, International Journal of Engineering Mathematics, Volume 2014 (2014), Article ID 485431, 12 pages.

D. Patel, M.K. Abeyratne, M.H.M.R. Shyamali Dilhani, Wavelet– Galerkin Solution for Boundary Value Problems International Journal of Engineering Research and Development e-ISSN: 2278-067X, p-ISSN: 2278-800X, www.ijerd.com Volume 10, Issue 5 (May 2014), PP.21-30

M.K. Abeyratne, M.H.M.R. Shyamali Dilhani, D. Patel "Wavelet-Galerkin Technique for Neumann-Helmholtz-Poisson Boundary Value problems" published at International Journal of Engineering Research and Development, Volume 10, Issue 5 (May 2014)

Dickson L.N, M.K.Abeyratne, Boundary Correction methods for non-parametric kernel smoothing methods 9th Science Symposium will be held in December 2012, Faculty of Science University of Ruhuna, Sri Lanka

M.C.S. Fernando, M.K.Abeyratne, Investigation of finite volume method with diffusion equation 8th Science Symposium will be held in December 2011, Faculty of Science Unicversity of Ruhuna, Sri Lanka

M.K.Abeyratne, C.I. Gomas, Finite difference methods for surface-ground water flow models, 7th Science Symposium, (Proceedings), 15th December 2010, Faculty of Science Unicversity of Ruhuna, Sri Lanka

P.Samarasekara, M.K.Abeyratne, P.L. Dilani, S. Dehipawalage Heisenberg Hamiltonian with Second Order Perturbation for Spinel Ferrite Ultra Thin films, E. Journal of Physics, 2009

M.K.Abeyratne, W.Freeden, Wavelet Applications generated by layer potentials and vector spherical harmonics for solving elliptic boundary value problems in linear elasticity and their applications in geoscience- present state of knowledge and future directions, Abstract, International conference on current trends in industrial and applied mathematics January 16-18, 2007, Department of Applied Mathematics, Faculty of Technology and Engineering, The M.S. University of Baroda, Gujarat, India.

M.K.Abeyratne, Cauchy-Navier Wavelet Solvers for the First Boundary Value Problem of Elastostatics. Proceedings of the 42th annual conference on Earth System Processes related to Earthquakes, Tsunamis and Volcanic Eruptions, Indian Geophysical Union, Barkathullah University, Bhopal, India, 2005.

M.K.Abeyratne, P.L.J.S.S. Liyanage, W.L.Asanthi, Nonparametric Regression Models for Fitting Data with Applications in Fisheries Biology. 3rd Science Symposium, Faculty of Science, University of Ruhuna, 2005.

L. W. Somathilake, J.M.J.J. Peiris, K. C. N. Shanthidevi, M.K.Abeyratne Pattern formation by Reaction Diffusion Systems, abstract on SLAAS, 60th Annual session, 2004.

L. W. Somathilake, J.M.J.J Peiris, K. C. N. Shanthidevi, M.K.Abeyratne, On some mathematical models arising in chemical kinetics, abstract on SLAAS, 60th Annual session, 2004.

M.K. Abeyratne, W. Freeden, C. Mayer, Multiscale Deformation Analysis by Cauchy-Navier Wavelets, Journal of Applied Mathematics, 5, 105-128, 2003.

The Educational Support Foundation - Ruhuna Mathematics (ESFoRuM)
In December 2004, just after the Tsunami, an organization has been formed by the members of the Department of Mathematics with the approval of the Council of the University of Ruhuna, named EsFoRuM. I have been working as the Co-Secretary of EsFoRuM. Under the ESFoRuM mainly the following activities were conducted:

  • Rehabilitation of more than 40 school libraries affected by Tsunami utilizing the funds received from Ministry of Foreign Affairs, Luxemburg Government. (Total budget : 48896 Euro)
  • Monthly Scholarship programme for school children who lost either father or mother due to Tsunami which is being financially supported by West Japan Scholarship Foundation, a group of Academics of the Department of Mathematics, University of Kaiserslautern and Rotary Club, Kaiserslautern, Germany, and many well-wishers in Germany and Japan.(about 400 scholarships, Rs. 1000 per month per student covering a period of 5 years)
  • Coordinate to award two gold medals to best Mathematics and Industrial Mathematics Graduates under the financial support of CIMPA France.(since 2005)


Umi-Matara Book Foundation
A voluntary organization has been formed by the members of the Department of Mathematics, University of Ruhuna in 1999 with the aim of donating books for school libraries in remote areas in the country. The foundation is named as Umi-Matara Book Foundation. This is established utilizing the financial support received from well-wishers in Umi-Machi, Japan under the coordination of a senior staff member of the Department of Mathematics. I have been working as the co-secretary of the Foundation. Foundation donates books for 2-3 schools per year since 2009 and the foundation has established about 40 school libraries during the period up to 2015.