Assistant Professor, Department of Mathematics, Mobile: GOA , India. Fax:

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1 Dr. P. Dhanumjaya Assistant Professor, Department of Mathematics, Mobile: BITS-Pilani, Goa Campus, GOA , India. Fax: Education : Ph.D, Dept of Mathematics, Indian Institute of Technology, Bombay. Dissertation: Finite Element Methods for the Extended Fisher-Kolmogorov(EFK) Equation : M.Sc(Tech), Dept of Mathematics, Jawaharlal Nehru Technological University, Hyderabad (Distinction with percentage of marks : 74%) : B.Sc(Mathematics, Physics, Chemistry), Silver Jubilee Residential Degree College, Kurnool, AP (Distinction with percentage of marks : 70%). Research Interest Computational Numerical Techniques Finite Element Methods Computational Partial Differential Equations Publications P. Danumjaya, Finite Element Methods for the one-dimensional Extended Fisher- Kolmogorov (EFK) Equation, Applied Mathematics and Computation(submitted) P. Danumjaya and Amiya K. Pani, Mixed Finite Element Methods for a fourth order reaction diffusion equation, Journal on Numerical Methods for Partial Differential Equations, DOI /num.20679,

2 P. Danumjaya and Hari Shanker Gupta, An ill-posed Cauchy problem for second order elliptic equation appearing in a sonic boom, Technical Report, IISc, Bangalore, P. Danumjaya and A. K. Nandakumaran, Orthogonal cubic spline collocation method for the Cahn-Hilliard equation, Applied Mathematics and Computation, 182 pp , P. Danumjaya and Amiya K. Pani, Numerical Methods for the Extended Fisher- Kolmogorov (EFK) equation, Int. Jour. Numer. Anal. Model. Vol 3, Number 2, pp , P. Danumjaya and Amiya K. Pani, Orthogonal Cubic Spline Collocation Method for the Extended Fisher-Kolmogorov (EFK) equation, Jour. of Comp and Appl. Math., Vol 174/1 pp , P. Danumjaya, An orthogonal cubic spline collocation method for the Fisher-Kolmogorov (FK) equation, Proceedings of International Conference and Instructional Workshop on Industrial Mathematics held December: 7 9, 2002, IIT Bombay, India. P. Danumjaya and Amiya K. Pani, Finite element method for the extended Fisher- Kolmogorov (EFK) equation, Proceedings of International Conference on Recent trends in Nonlinear Analysis and it s applications, held December: 15 17, 2001, IIT Kanpur, India. P. Danumjaya and Amiya K. Pani, Semidiscrete Galerkin Method for the Extended Fisher-Kolmogorov (EFK) equation, Proceedings of International Conference on Nonlinear Systems: Modelling, Simulation and Applications, held December: 26 29, 2000, Nanded, India. Thesis Abstract The main objective of the dissertation was to discuss the finite element Galerkin methods for the extended Fisher-Kolmogorov(EFK) equation. The EFK equation arises in a variety of applications such as pattern formation in bi-stable systems, propagation of domain walls in liquid crystals and travelling waves in reaction diffusion systems. Therefore four core methods were discussed in this dissertation. In the first method, a C 1 -conforming finite element method was analyzed for EFK equation. Since the EFK equation admits a Lyapunov functional, a priori bounds were established using the Lyapunov functional. Then existence, uniqueness and regularity results were derived for the EFK equation using Faedo-Galerkin method. Using piecewise polynomials of degree 3, we have established the optimal error estimates for 2

3 both semidiscrete scheme and completely discrete schemes. A few computational experiments were conducted. The C 1 -conforming finite element methods are computationally expensive duetoimpositionofc 1 -interelement continuity requirements anduseofhigher degree polynomials. Therefore the remaining part of the thesis was devoted to methods which violate C 1 -continuity condition and/or avoids using higher degree polynomials. To avoidtheinterelement C 1 -continuity condition, acommonapproachforthefourth order problem was to use a non-conforming finite element method. With the help of Morley nonconforming finite element, the optimal error estimates for the semidiscrete method was derived. A mixed finite element method which violates the inter-element C 1 -continuity requirement on the approximating spaces was used. First, the EFK equation was split into two second order equations by setting u = v. Then, C 0 -piecewise linear elements was used to approximating both u and v. Due to the different kinds of boundary conditions, two different problems (P 1 ) and (P 2 ) was set up. With the help of piecewise linear elements, a study of convergence analysis was undertaken. Then optimal error estimates were derived for the problem (P 1 ) using semidiscrete method and completely discrete methods. This includes backward Euler, Crank-Nicolson scheme and second order backward difference schemes. A certain modification of the usual Crank-Nicolson scheme was proposed to derive L p -bounds for the discrete solution using discrete Lyapunov functional. The semidiscrete error analysis for the problem P 2 and sub-optimal error estimates were discussed. Finally, the continuity condition was relaxed to allow for a discontinuous Galerkin finite element methods (DGFEM) for the EFK equation. The optimal error estimates were derived for the semidiscrete Galerkin scheme. The mixed discontinuous Galerkin finiteelement methodwasdiscussed fortheproblems(p 1 )and(p 2 ). Further, thea priori bounds for the discrete problem were derived and error estimates for the discontinuous Galerkin method were established. The concluding chapter made a critical assessment of the above points and proposed directions for the future research. Teaching Experience From 9th January, 2006 to till date I have been involved in teaching B.Tech and M.Sc(Hons.) students. I have taught several courses like: Mathematics I: Basic Calculus, Mathematics II: Linear Algebra & Complex Variables, 3

4 Mathematics III: Differential Equations Numerical Analysis (with Lab Component) Optimization Techniques Elementary Real Analysis Ordinary Differential Equations (with Lab Component) Partial Differential Equations (with Lab Component) Finite Difference Methods (with Lab Component) Finite Element Methods (with Lab Component) Scientific Computing Lab (MATHEMATICA): Solving differential equations using MATHEMATICA Scientific Computing Lab (MATLAB): Numerical solutions for partial differential equations using MATLAB Research Experience From 12th August 2004 to 03rd January 2006 I have worked as a Post-Doctoral Fellow at IISc Bangalore after my Ph.D thesis submission. I was involved Sonic Boom Problem which is a challenging research area. Invited Lectures Participated as Speaker and Resource Person for a National Program on Differential Equations: Theory, Computation and Applications, UG-Level Program at Birla Institute of Applied Sciences Bhimtal, Uttarakhand, during June Participated as Speaker and Resource Person for a National Program on Differential Equations: Theory, Computation and Applications, UG-Level Program at IMA Bhubaneshwar, during May Delivered a series of lectures to M.Sc and Ph.D Students on Scientific Computation at NIT Warangal from 30th January 2012 to 1st February

5 Delivered a series of lectures in National Workshop on Recent Trends in Mathematics held at Dept. of Mathematics, Mahatma Gandhi Vidyamandir, Nashik, during January 27-29, Delivered a series of lectures in National Workshop on Mathematical Softwares and Applications held at Dept. of Mathematics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad, during March 23-27, Delivered six lectures in Refresher Course at Dr. Babasaheb Ambedkar Marathwada University, Aurangabad, during March 3-5, Workshop Organization I have organized an Introductory Workshop on MATHEMATICA at BITS- Pilani, Goa Campus during July I have organized an Introductory Workshop on Scilab at BITS-Pilani, Goa Campus during 9-10 July I have delivered a series of lectures on Scilab and conducted lab sessions with hands on computation. I have organized one month International Workshop on Advances in Computational Partial Differential Equations(ACPDE-2011) at BITS-Pilani, Goa Campus during 7th February to 5th March I have delivered a series of lectures on Finite Difference Methods for the Differential Equations and conducted lab sessions with hands on computation. I have organized an Intensive Workshop on Scientific Computation at BITS- Pilani, Goa Campus during 20th July to 25th July I have delivered a series of lectures on Finite Difference Methods for Ordinary Differential Equations and Partial Differential Equations. In this workshop, we conducted lab sessions with hands on computation. Presentations in Conferences National Conference on New Vistas in Computational Fluid Dynamics in Engineering during 27-29th January 2012 held at NIT Warangal (NITW). Titke of the talk: Mixed Discontinuous Galerkin Finite Element Methods for the Extended Fisher-Kolmogorov (EFK) Equation. 5

6 International Conference on Scientific Computation, Numerical Analysis and Applications held during July: (2005), IISc Bangalore, India. Title of the talk: Orthogonal Cubic Spline Collocation Method for the Cahn- Hilliard Equation. International Conference on Recent trends on Applied mathematics held during December: (2004), IIT Bombay, India. Title of the talk: Mixed Finite Element Methods for the Extended Fisher- Kolmogorv (EFK) Equation. International Conference and Instructional Workshop on Industrial Mathematics held during December: 7 9 (2002), IIT Bombay, India. Title of the talk: An orthogonal Cubic Spline Collocation Method for the Fisher- Kolmogorov (FK) equation. International Conference on Recent trends in Nonlinear Analysis and it s applications, held during December: (2001), IIT Kanpur, India. Title of the talk: Finite Element Method for the Extended Fisher-Kolmogorov (EFK) equation. International Conference on Nonlinear systems: Modelling, Simulation and Applications, held during December: (2000), Nanded, India. Title of the talk: Semidiscrete Finite Element method for the Extended Fisher- Kolmogorov (EFK) equation. Abroad Visit I have visited Abdus Salam International Centre for Theoretical Physics (ICTP), Italy for attending Workshop on Modelling in Life and Material Sciences and in Technology held at Abdus Salam International Centre for Theoretical Physics (ICTP), Italy during 8th March 2004 to 2nd April Attended Workshops Workshop on Recent Trends in Partial Differential Equations and Applications during March 2012, held at Hyderabad Central University. Workshop on Scientific Computation, Numerical Analysis and Applications held from 24th January 2005 to 4th February 2005 at IISc Bangalore, India. 6

7 Indo-French workshop on Partial Differential Equations and their Applications held from 7th February 2005 to 12th February 2005 at IISc Bangalore, India. Workshop on Scientific Computation, Numerical Analysis and Applications held from 04th July 2005 to 15th July 2005 at IISc Bangalore, India. Workshop on Computational Partial Differential Equations (CPDE-05) held from 4th June 2005 to 24th June 2005 at IIT Bombay. Indo-French Workshop on Partial Differential Equations and their Applications held from 7th February 2005 to 12th February 2005 at IISc, Bangalore. Workshop on Scientific Computation, Numerical Analysis and Applications held from 24th January to 4th February 2005 at IISc, Bangalore. Workshop on Indo-UK Study Group Meeting on Industrial Problems held during December at IIT Bombay, India. NBHM sponsored workshop on Partial Differential Equations, Viscosity solutions and Applications, held from 21st July 2003 to 8th August 2003 at IISc, Bangalore. Indo-French Cyber workshop held during Feb at IISc, Bangalore. M.Sc(Hons) Projects Guidance Year 2009 Finite Element Methods for Fisher-Kolmogorov (FK) equation. B.Tech Projects Guidance Year 2010 Immersed Interface Method for Boundary Value Problems Year 2009 Relaxation Method for the Burger s equation. 7

8 Year 2008 Qualitative Theory for Differential Equations Finite Difference Methods for Elliptic Partial Differential Equations Finite Element Methods for Boundary Value Problems Numerical Solutions for Parabolic Partial Differential Equations Year 2007 Numerical solutions for Ordinary Differential Equations using MATLAB Finite Difference Methods for Partial Differential Equations Numerical solutions for Partial Differential Equations Technical Skills General Skills in Mathematics and computing. Specific expertise in: Mathematics: Orthogonal Cubic Spline Collocation Method, Radau 5 Computing platforms: UNIX, Windows 2000/NT Programming languages: FORTRAN, C and HTML Mathematical Softwares: Extensive experience with Matlab, Mathematica and Scilab moderate experience with Maple Text formatting and office computing: LaTeX, Word, Power point. Committees : Convener for cross campus department committee for academics(ccdca) : Department Research Committee Member at BITS-Pilani, Goa Campus. 8

9 : Department Faculty Recruitment Committee Member at BITS-Pilani, Goa Campus : Department Library Committee member. Doctoral Adivisory Committee member : Seminar Co-ordinator, Dept. of Mathematics, BITS-Pilani, Goa : Warden for UG boys hostel, BITS-Pilani, Goa : Post Graduate Student Committee, Dept of Mathematics, IIT Bombay : Department Representative for Research Scholar s Forum (RSF) : Hostel Secretary, A.P. Silver Jubilee Residential Degree College, Kurnool, Andhra Pradesh. Personal Details Name : Palla Danumjaya Place of Birth : Proddatur, Cuddapah (dist), A.P Sex : Male Nationality : Indian Marital Status :Married Present Address : Dept. of Mathematics, BITS-Pilani, Goa Campus, Zuarinagar, Goa, Goa , India. Phone : , Mobile:

CURRICULUM VITAE. Dept. of Mathematics, Sundergarh,Rourkela (Odisha) INDIA. Residential Address : C/O -BiswanathKar, At- Kodagambhir,

CURRICULUM VITAE. Dept. of Mathematics, Sundergarh,Rourkela (Odisha) INDIA. Residential Address : C/O -BiswanathKar, At- Kodagambhir, CURRICULUM VITAE RASMITA KAR Date of Birth : April 17, 1982 Nationality : Indian Gender : Female Marital status : Married Departmental Address : NIT Rourkela, Dept. of Mathematics, Sundergarh,Rourkela-769008