Arbaz Khan - Department of Mathematics,Indian Institute of Technology Roorkee
Arbaz Khan
Arbaz Khan Assistant professor arbaz@ma.iitr.ac.in Website
Areas of Interest
  • Numerical Solution of Partial Differential Equations, h-p finite element/Spectral Element Methods, Least Squares Method, Discontinuous Galerkin (DG) FEM, HDG FEM, A Posteriori Error Analysis, Multigrid Method, Parallel Computing, Domain Decomposition, Scientific Computing, Mixed FEM, Eigenvalue problems, Numerical Linear Algebra, Uncertainty Quantification, Stochastic Partial Differential Equation, Adaptivity
Professional Background
FromPeriodPositionOrganisation
2020-01-31OngoingAssistant ProfessorIIT Roorkee
2017-06-012 years 7 months 29 daysPDRAUniversity of Manchester, UK
2015-09-011 year 8 months 30 daysMATCH Postdoc FellowHeidelberg University, Germany
2015-01-307 months 1 dayInstitute Postdoc fellowIIT Kanpur
Multiple Posts
FromPeriodPositionOrganisation
2020-09-01OngoingMember, Departmental Research Committee (DRC)Department of Mathematics, IIT Roorkee
2020-09-01OngoingMember, Webinar committeeDepartment of Mathematics, IIT Roorkee
2020-09-07OngoingDeputy Coordinator, Annual Report & WebsiteDepartment of Mathematics, IIT Roorkee
2020-09-07OngoingDeputy Coordinator, Seminar (Faculty, Visitor)Department of Mathematics, IIT Roorkee
2011-08-011 year 11 months Member, Departmental Post Graduate CommitteeDepartment of Mathematics & Statistics, IIT Kanpur
Honors and Awards
AwardInstituteYear
Associate FellowThe Higher Education Academy, UK2019
Educational Details
DegreeSubjectUniversityYear
PhDApplied MathematicsIndian Institute of Technology Kanpur, India2015
Sponsored Research Projects
TopicFunding AgencyStart DatePeriod
A fast and efficient numerical method for convection dominated problems on parallel computersSRIC, IIT Roorkee2020-10-12Ongoing
Analysis of an efficient and fast numerical method for poroelasticity with uncertain inputsSERB-DST (MATRICS)2020-12-29Ongoing
Memberships
  • SIAM, Member
  • SIAG UQ, Member
  • SIAG on Analysis of Partial Differential Equations, Member
  • Ramanujan Mathematical Society, Member
Teaching Engagements
TitleCourse CodeClass NameSemester
Advanced Numerical AnalysisMAN-902Pre-PhDAutumn
Theory of Differential EquationsMAN-903Pre PhdSpring
Numerical MethodsMAN-004Ist yearSpring
PHDs Supervised
TopicScholar NameStatus of PHDRegistration Date
Numerical Solution of PDEsAparna BansalO2020-08-17
Numerical Sol of PDEsSumit MahajanO2021-02
Visits to outside institutions
Institute VisitedPurpose of VisitDate
Isaac Newton Institute for Mathematical Sciences, University of Cambridge, UKResearch collaboration2018-04-29
School of mathematics, University of Birmingham, UKResearch collaboration2018-03-27
Referred Journal Papers
  • A nonsymmetric approach and a quasi-optimal and robust discretization for the Biot's model. Part I--Theoretical aspects, Arbaz Khan, Pietro Zanotti, American Mathematical Society, 2021 , Mathematics of Computation
  • Robust a posteriori error analysis for rotation-based formulations of the elasticity/poroelasticity coupling, Veronica Anaya, Arbaz Khan, David Mora, Ricardo Ruiz-Baier, arXiv, 2021 , arXiv:2106.09074 , 23 pages
  • Divergence-conforming methods for transient doubly-diffusive flows: A priori and a posteriori error analysis, Raimund Bürger, Arbaz Khan, Paul E. Méndez, Ricardo Ruiz-Baier, Under review, 2021 , arxiv preprint
  • Conforming, nonconforming and DG methods for the stationary generalized Burgers-Huxley equation, A Khan, MT Mohan, R Ruiz-Baier, Springer, 2021 , Journal of Scientific Computing , 52 vols , 88 pages
  • Parameter-robust stochastic Galerkin approxination for linear poroelasticity with uncertain inputs, A. Khan, C. E. Powell, SIAM, 2021 , SIAM Journal on Scientific Computing (SISC) , 43(4) vols , B855-B883 pages
  • Robust a posteriori error estimation for mixed finite element approximation of linear poroelsticity,, A. Khan, D. J. Silvester, Oxford University Press, 2021 , IMA Journal of Numerical Analysis , 41(3) vols , 2000-2025 pages
  • Robust a posteriori error estimation for stochastic Galerkin formulations of parameter-dependent linear elasticity equations, A. Khan, A. Bespalov, C. E. Powell, D. J. Silvester, American Mathematical Society, 2021 , Mathematics of Computation , 90 vols , 613-636 pages
  • Divergence-conforming discontinuous Galerkin finite elements for Stokes eigenvalue problems, J. Gedicke, A. Khan, Springer, 2020 , Numerische Mathematik , 144 vols , 585-614 pages
  • Spectral method and spectral element method for three dimensional linear elliptic system: analysis and application, A. Khan, Springer, 2020 , Journal of Scientific Computing , 82 vols , 1-32 pages
  • A robust a posteriori error estimator for Divergence-conforming DG methods for Oseen equation, A. Khan, G. Kanschat, SIAM, 2020 , SIAM Journal on Numerical Analysis (SINUM) , 58(1) vols , 492-518 pages
  • On the generalized Burgers-Huxley equation: Existence, uniqueness, regularity, global attractors and numerical studies, Manil T Mohan, Arbaz Khan, American Institute of Mathematical Sciences, 2020 , Discrete & Continuous Dynamical Systems - B , 46 pages
  • Robust Preconditioning for stochastic Galerkin formulations of parameter-dependent linear elasticity equations, A. Khan, C. E. Powell, D. J. Silvester,, SIAM, 2019 , SIAM Journal on Scientific Computing (SISC) , 41(1) vols , A402-A421 pages
  • Arnold-Winther Mixed Finite Elements for Stokes Eigenvalue Problems, J. Gedicke, A. Khan, SIAM, 2018 , SIAM Journal on Scientific Computing (SISC) , 40(5) vols , A3449-A3469. pages
  • Robust A Posteriori Error Estimators for Mixed Approximation of Nearly Incompressible Elasticity, A. Khan, C. E. Powell, D. J. Silvester, Wiley, 2019 , International Journal for Numerical Methods in Engineering (IJNME) , 119 vols , 18-37 pages
  • Spectral element method for parabolic interface problems, A. Khan, C. S. Upadhyay, M. I. Gerristma, Elsevier, 2018 , Computer Methods in Applied Mechanics and Engineering (CMAME) , 317 vols , 66-94 pages
  • Spectral Element Method for parabolic initial value problem with non-smooth data: analysis and application, A. Khan, P. Dutt, C. S. Upadhyay, Springer, 2017 , Journal of Scientific Computing , 73(2-3) vols , 876-905 pages
  • Least-squares spectral element preconditioners for fourth order elliptic problems, A. Hussain, A. Khan, Elsevier, 2017 , Computers and Mathematics with Applications , 74(3) vols , 482-503 pages
  • Spectral Element Method for Three Dimensional Elliptic Problems with Smooth Interfaces, A. Khan, A. Hussain, S. Mohapatra, C. S. Upadhyay, Elsevier, 2017 , Computer Methods in Applied Mechanics and Engineering (CMAME) , 315 vols , 522-549 pages
  • Exponentially accurate spectral element method for fourth order elliptic problems, A. Khan, A. Hussain, Springer, 2017 , Journal of Scientific Computing , 71(1) vols , 303-328 pages
  • Exponentially accurate nonconforming least-squares spectral element method for elliptic problems on unbounded domains, A. Khan, C. S. Upadhyay, Elsevier, 2016 , Computer Methods in Applied Mechanics and Engineering (CMAME) , 305 vols , 607-633 pages
  • Nonconforming Least-Squares Spectral Element Method for European options, A. Khan, P. Dutt, C. S. Upadhyay, Elsevier, 2015 , Computers and Mathematics with Applications , 70(1) vols , 47-65 pages
  • Importance of Molecular Heat Convection in Time Resolved Thermal Lens Study of Highly Absorbing Samples, P. Kumar, A. Khan, D. Goswami, Elsevier, 2014 , Chemical Physics , 441 vols , 5-10 pages
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