Christina C. Christara

Research specialisation and interests Scientific computing, computational mathematics Numerical methods, analysis and computation Parallel computation High Performance Computing Mathematical software Numerical solution of Partial Differential Equations Solution of large sparse linear systems Numerical weather and climate prediction Applications of numerical methods to science, engineering and finance

Current position: Associate Professor

Degrees

Ph.D.	Computer Science	Purdue University	W. Lafayette, Indiana, U.S.A.	1988
M.Sc.	Computer Science	Purdue University	W. Lafayette, Indiana, U.S.A.	1986
B.Sc.	Mathematics	Aristotle University	Thessaloniki, Greece	1982

Courses

• Spring 2013
  • CSC336: Numerical methods
• Fall 2012
  • CSC350: Numerical Algebra and Optimisation
  • CSC456-2306: High Performance Scientific Computing
• Spring 2012
  • CSC336: Numerical methods
• Fall 2011
  • CSC350: Numerical Algebra and Optimisation
  • CSC2321: Matrix Calculations
• Spring 2009
  • CSC351: Numerical Approximation, Integration and Ordinary Differential Equations
  • CSC446-2310: Computational Methods for Partial Differential Equations
• Fall 2008
  • CSC260: Introduction to Scientific, Symbolic and Graphical Computation
• Past Courses

Selected Publications

• Adaptive and high-order methods for valuing American options, Christina Christara and Duy Minh Dang
• A PDE Pricing Framework for Cross-Currency Interest Rate Derivatives, Duy Minh Dang, Christina Christara, Kenneth R. Jackson and Asif Lakhany
• Quartic spline collocation for second-order boundary value problems, Christina C. Christara and Guohong Liu
• Quadratic spline collocation for one-dimensional linear parabolic partial differential equations, Christina C. Christara, Tong Chen and Duy Minh Dang
• Quartic spline collocation for fourth-order boundary value problems, Christina C. Christara, Ying Zhu and Jingrui Zhang
• Spline collocation for parabolic partial differential equations, Christina C. Christara, Tong Chen and Duy Minh Dang
• A High-Performance Method for the Biharmonic Dirichlet Problem on Rectangles, Christina C. Christara and Jingrui Zhang
• Optimal Quadratic and Cubic Spline Collocation on Nonuniform Partitions, Christina C. Christara, and Kit Sun Ng
• Adaptive Techniques for Spline Collocation, Christina C. Christara, and Kit Sun Ng
• GIA-induced secular variations in the Earth's long wavelength gravity field: Influence of 3-D viscosity variations (short communication), Konstantin Latychev, Jerry X. Mitrovica, Mark E. Tamisiea, Jeroen Tromp, Christina C. Christara and Robert Moucha
• Glacial isostatic adjustment on 3-D Earth models: a finite-volume formulation, Konstantin Latychev, Jerry X. Mitrovica, Jeroen Tromp, Mark E. Tamisiea, Dimitri Komatitsch, and Christina C. Christara
• Optimal Quadratic Spline Collocation on Non-Uniform Partitions, Christina C. Christara, and Kit Sun Ng
• Optimal Cubic Spline Collocation on Non-Uniform Partitions, Christina C. Christara, and Kit Sun Ng
• Quadratic Spline Galerkin Method for the Shallow Water Equations, Anita T. Layton, Christina C. Christara, and Kenneth R. Jackson
• Optimal Quadratic Spline Collocation Methods for the Shallow Water Equations, Anita T. Layton, Christina C. Christara, and Kenneth R. Jackson
• Quadratic Spline Collocation Revisited: Extension to Systems of Elliptic PDEs, Christina C. Christara and Kit Sun Ng
• Fast Fourier Transform Solvers and Preconditioners for Quadratic Spline Collocation, Christina C. Christara and Kit Sun Ng
• An Efficient Transposition Algorithm for Distributed Memory Computers, C. Christara, X. Ding and K. R. Jackson
• Multigrid and Multilevel Methods for Quadratic Spline Collocation, Christina C. Christara and Barry Smith
• Parallel solvers for spline collocation equations, C. C. Christara
• Quadratic spline collocation methods for elliptic partial differential equations, C. C. Christara
• High performance computing of elliptic partial differential equations with spline collocation, C. C. Christara
• Parallel computation of partial differential equations on distributed memory machines, C. C. Christara
• Multicolour orderings and iterative methods for elliptic equations, C. C. Christara
• Domain decomposition and incomplete factorisation methods for partial differential equations, C. C. Christara
• Schur complement preconditioned conjugate gradient methods for spline collocation equations, C. C. Christara
• Conjugate gradient methods for spline collocation equations, C. C. Christara
• A Domain Decomposition Spline Collocation Method for Elliptic Partial Differential Equations, C. C. Christara and E. N. Houstis
• A Parallel Spline Collocation - Capacitance Method for Elliptic Partial Differential Equations, C. C. Christara, E. N. Houstis and J. R. Rice
• Geometry Decomposition based Methods for solving Elliptic Partial Differential Equations, C. C. Christara, A. Hadjidimos, E. N. Houstis, J. R. Rice and E. A. Vavalis
• Quadratic Spline Collocation Methods for two point boundary value problems, E. N. Houstis, C. C. Christara and J. R. Rice
• Performance of Scientific Software, E. N. Houstis, J. R. Rice, C. C. Christara and E. A. Vavalis
• Scientific Computing by Numerical Methods, C. C. Christara and K. R. Jackson

Supervised students' theses

• ``A study of a discrete element method based granular dynamics solver'', Tina Yee, M.Sc. thesis, University of Toronto, 2009, 43 pages.
• ``Multigrid and Spline Collocation Methods on Non-uniform Grids'', Guoyu Wang, M.Sc. thesis, University of Toronto, September 2008, 98 pages.
• ``Bi-quartic Spline Collocation Methods for Fourth-order Boundary Value Problems with an Application to the Biharmonic Dirichlet Problem'', Jingrui Zhang, Ph.D. thesis, University of Toronto, January 2008, 160 pages.
• Adaptive Finite Difference Methods for Valuing American Options, Duy Minh Dang, M.Sc. Thesis
• Quartic Spline Collocation Methods For Second-Order Two-Point Boundary Value ODE Problems, Guohong Liu, M.Sc. Thesis
• Pricing Convertible Bonds with Dividend Protection subject to Credit Risk Using a Numerical PDE Approach, Qingkai Mo, M.Sc. Thesis
• An Efficient Algorithm Based on Quadratic Spline Collocation and Finite Difference Methods for Parabolic Partial Differential Equations, Tong Chen, M.Sc. Thesis
• Pricing Convertible Bonds using Partial Differential Equations, Lucy Xingwen Li, M.Sc. Thesis
• Spline Collocation on Adaptive Grids and Non-Rectangular Domains, Kit Sun Ng, Ph.D. Thesis
• Multigrid and Cubic Spline Collocation Methods for Advection Equations, Zheng Zeng, M.Sc. Thesis
• Towards a high-performance method for the biharmonic Dirichlet problem, Jingrui Zhang, Research Paper (equivalent to M.Sc. Thesis)
• Quartic-Spline Collocation Methods for Fourth-Order Two-Point Boundary Value Problems, Ying Zhu, M.Sc. Thesis
• High-Order Spatial Discretization Methods for the Shallow Water Equations, Anita W. Tam, Ph.D. Thesis, co-supervised by Ken Jackson
• Quadratic Spline Collocation Methods for Systems of Elliptic PDEs, Kit Sun Ng, M.Sc. Thesis
• Numerical Solution of the Shallow-Water Equations on Distributed Memory Systems, Xiaoliang (Lloyd) Ding, M.Sc. Thesis, co-supervised by Ken Jackson
• Fast Fourier transform solvers for quadratic spline collocation, Athanasia Constas, M.Sc. Thesis

Other publications of possible interest

• A brief introduction to MATLAB, Christina C. Christara and Winky Wai
• Tutorial on MATLAB, Christina C. Christara
• A brief introduction to MAPLE, Christina C. Christara
• Tutorial on MAPLE, Christina C. Christara
• Starting on Latex, Christina C. Christara (includes some tips on MATLAB plots)

You may also be interested in looking at the www site of the Numerical Analysis and Scientific Computing Group of the Department of Computer Science at the University of Toronto. Alternatively, you have anonymous ftp access to the respective ftp site, by connecting to ftp.cs.toronto.edu, logging in as anonymous and changing to directory na.

Contact infomation:

E-mail:	ccc SYMBOL_AT cs DOT toronto DOT edu
Telephone number:	+1 416 978 7360
Fax number:	+1 416 946 7132 or +1 416 978 1931
Office:	BA 4226, Bahen Center for Information Technology, 40 St. George Street
Mailing address:	Professor Christina Christara Department of Computer Science University of Toronto 10 King's College Road Toronto, Ontario M5S 3G4 Canada

Visiting our department?
Driving and other travel directions are available.
Some information about accommodation near the campus is also available. (May be a bit outdated.)