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: Professor
CV
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
Selected Publications

Analysis of quantization error in financial pricing
via finite difference methods,
Christina C. Christara and Nat ChunHo Leung

Partial Differential Equation pricing of contingent claims
under stochastic correlation,
Nat ChunHo Leung, Christina C. Christara and DuyMinh Dang

Spread option pricing using ADI methods,
Vida HeidarpourDehkordi and Christina C. Christara

PDE option pricing with variable correlations,
Christina C. Christara and Nat ChunHo Leung

Option pricing in jump diffusion models with
quadratic spline collocation,
Christina C. Christara and Nat ChunHo Leung

An efficient numerical PDE approach for pricing foreign exchange
interest rate hybrid derivatives,
Duy Minh Dang, Christina C. Christara, Kenneth R. Jackson and Asif Lakhany

Graphics processing unit pricing
of exotic crosscurrency interest rate derivatives with a
foreign exchange volatility skew model,
Duy Minh Dang, Christina C. Christara and Kenneth R. Jackson

A Highly Efficient Implementation on GPU Clusters of
PDEBased Pricing Methods for
PathDependent Foreign Exchange Interest Rate Derivatives,
Duy Minh Dang, Christina C. Christara and Kenneth R. Jackson

An Efficient GPUBased Parallel Algorithm for
Pricing MultiAsset American Options,
Duy Minh Dang, Christina C. Christara and Kenneth R. Jackson

Adaptive and highorder methods for valuing American options,
Christina C. Christara and Duy Minh Dang

A Parallel Implementation on GPUs of ADI Finite Difference Methods
for Parabolic PDEs with Applications in Finance,
Duy Minh Dang, Christina C. Christara and Kenneth R. Jackson

A PDE Pricing Framework for CrossCurrency Interest Rate Derivatives,
Duy Minh Dang, Christina C. Christara, Kenneth R. Jackson and Asif Lakhany

Pricing MultiAsset American Options on Graphics
Processing Units Using a PDE Approach,
Duy Minh Dang, Christina C. Christara and Kenneth R. Jackson

Quartic spline collocation for secondorder boundary value problems,
Christina C. Christara and Guohong Liu

Quadratic spline collocation for onedimensional
linear parabolic partial differential equations,
Christina C. Christara, Tong Chen and Duy Minh Dang

Quartic spline collocation for fourthorder boundary value problems,
Christina C. Christara, Ying Zhu and Jingrui Zhang

A HighPerformance 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

GIAinduced secular variations in the Earth's long wavelength
gravity field: Influence of 3D viscosity variations
(short communication),
Konstantin Latychev, Jerry X. Mitrovica, Mark E. Tamisiea, Jeroen Tromp,
Christina C. Christara and Robert Moucha

Glacial isostatic adjustment on 3D Earth models: a finitevolume formulation,
Konstantin Latychev, Jerry X. Mitrovica, Jeroen Tromp, Mark E. Tamisiea,
Dimitri Komatitsch, and Christina C. Christara

Optimal Quadratic Spline Collocation on NonUniform Partitions,
Christina C. Christara, and Kit Sun Ng

Optimal Cubic Spline Collocation on NonUniform 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

Numerical Methods for Pricing MultiAsset Options,
Yuwei Chen, M.Sc. thesis, University of Toronto,
January 2018, 75 pages.

``PDE option pricing: analysis and application
to stochastic correlation'',
Nat ChunHo Leung, Ph.D. thesis, University of Toronto,
June 2017, 119 pages.

``Efficient and accurate numerical PDE methods
for pricing financial derivatives'',
Mufan (Bill) Li, B.A.Sc. thesis, University of Toronto,
April 2015, 35 pages.

``Modeling multifactor financial derivatives
by a Partial Differential Equation approach
with efficient implementation on Graphics Processing Units'',
Duy Minh Dang, Ph.D. thesis, University of Toronto,
August 2011, 228 pages.

``A study of a discrete element method based granular dynamics solver'',
Tina Yee, M.Sc. thesis, University of Toronto, September 2009, 43 pages.

``Multigrid and Spline Collocation Methods on Nonuniform Grids'',
Guoyu Wang, M.Sc. thesis, University of Toronto, September 2008, 98 pages.

``Biquartic Spline Collocation Methods for Fourthorder
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, University of Toronto,
September 2007, 119 pages.

Quartic Spline Collocation Methods For SecondOrder TwoPoint
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 NonRectangular Domains,
Kit Sun Ng, Ph.D. Thesis

Multigrid and Cubic Spline Collocation Methods for Advection Equations,
Zheng Zeng, M.Sc. Thesis

Towards a highperformance method for the biharmonic Dirichlet problem,
Jingrui Zhang, Research Paper (equivalent to M.Sc. Thesis)

QuarticSpline Collocation Methods for FourthOrder TwoPoint
Boundary Value Problems,
Ying Zhu, M.Sc. Thesis

HighOrder Spatial Discretization Methods for the Shallow Water
Equations,
Anita W. Tam, Ph.D. Thesis, cosupervised by Ken Jackson

Quadratic Spline Collocation Methods for Systems of Elliptic PDEs,
Kit Sun Ng, M.Sc. Thesis

Numerical Solution of the ShallowWater Equations on Distributed
Memory Systems,
Xiaoliang (Lloyd) Ding, M.Sc. Thesis, cosupervised by Ken Jackson

Fast Fourier transform solvers for quadratic spline collocation,
Athanasia Constas, M.Sc. Thesis
Other publications of possible interest
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:
Email:
 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.)