# Natasha Flyer

- About Natasha
- Curriculum Vitae
- Publications
- Invited Talks
- Research Interest

### NATASHA FLYER

Institute for Mathematics Applied to Geosciences

Phone: (303) 497-1292

NCAR E-mail: flyer@ucar.edu

Boulder, CO 80305 URL: http://www2.image.ucar.edu/staff/flyer

EDUCATION

1999 Ph.D. University of Michigan, Ann Arbor (Atmospheric & Space Science, Scientific Computing)

1993 B.A. Northwestern University, Evanston, IL (Geological Sciences, Applied Math)

PROFESSIONAL APPOINTMENTS

2010-present Scientist III

National Center for Atmospheric Research (NCAR)

2006-2010 Scientist II

NCAR

2003-2006 Scientist I

NCAR

2000-2003 NSF Postdoctoral Fellow, Department of Applied Mathematics

University of Colorado, Boulder

1999-2000 Advanced Study Postdoctoral (ASP) Fellow

NCAR, Boulder, CO

1995-1998 NASA Graduate Student Research (GRFP) Fellow

University of Michigan, Ann Arbor

ADJUNCT/AFFILIATED PROFESSOR POSITIONS

2011-present Dept. of Scientific Computing, Florida State University

2011-present Dept. of Mathematics, Boise State University

2007-present Dept. of Applied Mathematics, University of Colorado-Boulder

2007-present Div. of Scientific Computing, Uppsala University, Sweden

2006-present Dept. of Mathematics, Kyungpook National University, Daegu, South Korea

COMMUNITY SERVICE

**1. National and international panels, advisory boards, and review committees**

- The National Academies of Science, Engineering, and Medicine 2007, 2008, 2009, 2010

- NSF/Division of Mathematical Sciences: Applied Mathematics 2008, 2009, 2010, 2011

- NSF/Division of Geosciences: 2008, 2011

- NASA: 2005, 2006

- National Research Foundation of South Africa: Applied Mathematics 2006, 2011

**2. Conference/Mini-Symposium Organizer**

- Committee member, Organizing committee, Korean SIAM Spring Conference, 2006

- Committee member, Organizing committee, PDEs on a Sphere, Santa Fe, NM, 2009

- Organizer, Mini-symposium, “Radial Basis Functions on the Sphere for Geophysical Applications”, SIAM Computational Issues in the Geosciences, Santa Fe, NM, 2007

- Organizer, Mini-symposium, “Workshop on Petascale Computing: Its impact on geophysical modeling and simulation”, May, TOY 2008

- Organizer, Mini-symposium, “Advanced techniques in radial basis function approximation for PDEs, Parts I & II ”, European Conference on Numerical Mathematics and Advanced Applications (ENUMATH), Sweden, 2009

- Organizer, NCAR workshop, “Numerical Methods for Free-Boundary Problems”, 2009

**3. Journal Referee**

Referee for over 20 journals such as:

SIAM journals (Applied Math, Numerical Analysis, Scientific Computing) Elsevier journals such as Journal of Computational Physics, IMA Journals (Oxford Press), Proceedings of the Royal Society A, AMS journals such as Mathematics of Computation, etc.

Average referee rate: 2 papers per month

**4. Student and Academic Program Advising**

**Postdoctoral Mentoring/Funding:**

1. **Cecile Piret**, ASP NCAR (funded 1/3 of salary from 2008-2010)

2. **Anders Malmberg**, Geophysical Statistics Project (GSP), NCAR (2007-2008)

**Ph. D Student Co-Advisor/Funding:**

1.** Julia Zuev**, Dept. of Applied Math, CU - Boulder (defended May 2007)

2. **Cecile Piret**, Dept. of Applied Math, CU - Boulder (defended December 2007)

3. **Lei Wang**, Dept. of Math, University of Michigan – Ann Arbor (2007, funded 1 year)

4. **Ben Jamroz**, Dept. of Applied Math, CU-Boulder (defended April 2009, funded 1.5 years)

5.** Zhen Qin**, Institute of Scientific Computing & Applied Math, Indiana Univ.-Bloomington (funded 1 month, defended May 2011)

6. **Evan Bollig**, Dept. of Scientific Computing, Florida State University 2010 (funded Summer 2010, 2011, will defend August 2012)

7. **Erik Lehto**, Division of Scientific Computing, Uppsala University, Sweden (funded for 3 years, will defend Sept. 2012)

**Master Students Co-Advisor/Funding:**

1.** Joe Lohemeier**, Dept. of Math, Boise State University, Idaho (funded Summer 2010, MSc defended Master’s thesis May 2011)

2. **Christopher-Ian Davis**, Dept. of Applied Math, CU-Boulder (MSc, defended April 2011)

3. **Colin Powell**, Dept. of Applied Math, CU-Boulder (MSc, defended November 2011)

**5. Education Outreach Activities**

**University Level:**

- Conduct a joint research group on radial basis functions with Bengt Fornberg at the University of Colorado-Boulder, Department of Applied Mathematics

- NCAR representative, Colorado Conference for Women in Computing, 2011

- Panelist, Colorado Conference for Women in Computing, 2008, “What a Ph.D. gets you?” Boulder, CO

- Undergraduate Project Mentor, Department of Physics, University of Colorado -Boulder, 2004.

- Talk, “The role of science and technology in today’s society”, University of Denver School of Business, 2004**K-12 educational activities:**

- Talk, “Applications of mathematics at NCAR”, Adams High School Math Club, 2005

- Talk, “Applied math in the geosciences”, Colorado High School Honors Institute, Boulder, CO, 2005 and 2006

- Science fair judge, Peak-to-Peak Academy, Lafayette, CO, 2007, 2008

- Regular volunteer for Education and Outreach Program at NCAR

AWARDS

Fall 2010 |
University of Oxford Research Fellowship Oxford Centre for Collaborative Applied Mathematics, UK |

Spring 2009 |
University of Oxford Research Fellowship Oxford Centre for Collaborative Applied Mathematics, UK |

1998 | University of Michigan Distinguished Achievement Award |

1995- 1998 | NASA Graduate Student Research Fellowship (4 awarded in the USA in 1995) |

1993 | Phi Beta Kappa Honor Society |

1993 | Northwestern University Award for Outstanding Scientific Accomplishment |

**INVITED TALKS**

1. “Radial basis functions: A new technique for solving PDEs ”, Dept. of Applied Mathematics, University of Colorado, Boulder, 2002.

2. “Corner singularities for initial -boundary value problems - Illustration and remedy for convectivediffusive

equations”, Department of Mathematics, Hong Kong Baptist University, March 2002.

3. “Convergence of spectral and finite-difference methods for initial-boundary value problems”,

Department of Mathematics, Hong Kong Baptist University, June 2002.

4. “Accurate numerical resolution of transients for convection-diffusion equations”, Department of

Scientific Computing, Uppsala University, Sweden, June 2002.

5. “The elusive time-space corner singularity: The nature of initial-boundary value problems”, Korean

Advanced Institute of Science and Technology (KAIST), Taegon, South Korea, March 2004.

6. “Radial basis functions: The basics and why they are hot”, 12th Applied Math Forum of South Korea,

March 2004, (Plenary speaker)

7. “The elusive time-space corner singularity: The nature of initial-boundary value problems”,

Department of Mathematics, Kyungpook National University, Daegu, South Korea, March 2004.

8. “The elusive time-space corner singularity: The nature of initial-boundary value problems”, Colorado

School of Mines, May 2004.

9. “Applications of asymptotics to geophysical fluid dynamics”, Division of Scientific Computing,

Uppsala University, Sweden, June 2005.

10. “The nature of initial-boundary value problems and their ramifications on high order methods”,

Department of Mathematics, University of Utah, Salt Lake City, January 2006.

11. “Solving hyperbolic PDEs in spherical geometry with radial basis functions”, Korean SIAM Annual

Meeting, Daegu, South Korea, May, 2006. http://ksiam.org/conference/annual061/index.html

(Plenary speaker)

12. “Transport schemes on a sphere using radial basis functions”, Division of Scientific Computing,

Uppsala University, Sweden, June 2006.

13. “Modeling simple atmospheric flows on a sphere using radial basis functions”, Department of

Applied Math, University of Colorado, Boulder, April 2007.

14. “The character of initial-boundary value problems and their numerical solution”, Wichita State

University, Kansas, August 2007.

15. “The character of initial-boundary value problems and their numerical solution”, University of

Cambridge, Department of Applied Mathematics and Theoretical Physics, UK, September 2007.

(Plenary speaker)

16. “Geophysical modeling using radial basis functions”, Division of Scientific Computing, Uppsala

University, Sweden, May 2008.

17. “Geophysical modeling using radial basis functions”, Max Planck Institute for Plasma Physics,

Garching, Germany, June 2008.

18. “Moving vortices on a sphere: Local node refinement for radial basis functions”, SIAM Annual

Meeting, San Diego, CA, July 2008.

19. “A radial basis function shallow water model and local refinement”, Los Alamos, NM, Sept. 2008.

20. “Geophysical modeling using radial basis functions”, University of Wyoming, October 2008.

21. “Applications of radial basis functions to solid earth geophysics”, SANUM (South African

Symposium on Numerical and Applied Mathematics), University of Stellenbosch, South Africa, April

2009 (Plenary speaker)

22. “Applications of radial basis functions to modeling atmospheric flows”, Department of Atmospheric,

Oceanic, & Planetary Physics, University of Oxford, UK, May 2009.

23. “Radial basis functions methods for modeling atmospheric and solid earth flows”, Mathematical

Institute, University of Oxford, UK, June 2009. http://www.maths.ox.ac.uk/node/9277

24. “Modeling mantle convection in a 3-D spherical shell with a hybrid radial basis function method”,

ENUMATH (European Conference on Numerical Mathematics and Advanced Applications), Uppsala

University, Sweden, July 2009. http://www.enumath.eu/link/uppsala.html

25. “Radial basis function methods for the geosciences”, Illinois Institute of Technology, October 2009.

26. “The elusive time-space corner singularity: The hidden nature of initial-boundary value problems and

its impact on numerics”, University of Indiana, Bloomington, IN, October 2009.

27. “Radial basis function methods for geofluid modeling”, Institute for Mathematics and its Applications

(IMA), University of Minnesota, Minneapolis-St. Paul, MN, April 2010

http://www.ima.umn.edu/videos/index.php?id=1224 (web – casted)

28. “A hybrid analytical-numerical method for evolutionary PDEs”, International Centre for

Mathematical Sciences (ICMS), Edinburgh, UK May 2010 (Plenary Speaker)

http://www.icms.org.uk/workshop.php?id=125]presentations

29. “The Gibbs phenomenon for radial basis functions”, SIAM Annual Meeting, July 2010.

30. “Recent developments in radial basis functions”, SIAM Annual Meeting, July 2010.

31. “Resolving planetary-scale flows with radial basis functions”, SIAM Annual Meeting, July 2010.

32. “The elusive time-space corner singularity: The hidden nature of initial-boundary value problems

and its impact on numerics”, University of Kent, Oct. 2010

33. “The hidden nature of initial-boundary value problems and its impact on numerics”, University of

Oxford, UK, Oct. 2010

34. “Radial basis function methods for computational geosciences”, Arizona State University April 2011

http://math.asu.edu/node/3333

36. “Radial basis functions for computational geoscience”, Current challenges in climate modelling 2011,

Uppsala University, Sweden, May 26-27, 2011 (Plenary Speaker),

http://www2.math.uu.se/cim/events/abstract_climate_Flyer.html

35. NSF/CBMS Regional Conference in the Mathematical Sciences-“Radial Basis Functions”, University

of Massachusetts-Dartmouth, Dept. of Mathematics, June 2011 (Principal Lecturer – 5 lectures,

funded by grant from NSF) http://www.umassdcomputing.org/conference/rbfcbms2011/

GRANTS (listed in order of award amount)

NSF PetaApps, Office of CyberInfrastructure (NSF-OCI 0904599) 2009-2012

Title: Collaborative Research: A multiscale unified simulation environment for geoscientific

applications

PI: Natasha Flyer

Co-investigative universities: University of Wyoming, Virginia Tech

Total Award: $1,000,000 NCAR Sub-Award: $ $616,822

NSF Collaboration in Mathematical Geosciences (NSF-DMS 0934317) 2009-2013

Title: Fast and Efficient Radial Basis Function Algorithms for Geophysical Modeling on Arbitrary

Geometries

PI: Natasha Flyer

Co-investigative universities: Boise State, Florida State, U. of Minnesota, U. of California-Davis

Total Award: $1,000,000 Each Sub-Award: $200,000

NSF Collaboration in Mathematical Geosciences (NSF-ATM 0620100) 2006-2011

Title: Freedom from Coordinate Systems, and Spectral Accuracy with Local Refinement: Radial

Basis Functions for Climate and Space-Weather Prediction

PI: Natasha Flyer

Co-investigative universities: Arizona State, U. of Colorado-Boulder, Boise State, U. of Michigan

Total Award: $513,152 NCAR Sub-Award: $317,171

NSF/NCAR Opportunity Fund 2005-2008

Title: Developing High-Precision Numerical Prototypes for Space-Weather Prediction

PI: Natasha Flyer

Award: $163,450

NSF Small Grants for Exploratory Research (SGER) 2006-2007

Title: Coronal Mass Ejection Initiations as a Result of Magnetic Helicity Accumulation in the Solar

Corona

PI: Mei Zhang , Co-PIs: Joan Burkepile, Natasha Flyer, B.C. Low (All NCAR personnel)

Award: $23,780

TEACHING EXPERIENCE

As an NSF postdoctoral fellow at the University of Colorado-Boulder, Department of Applied Mathematics,

I taught one class per semester during the academic year.

1. Developed upper level undergraduate course, “Introduction to Scientific Computing”, at the University

of Colorado-Boulder, Department of Applied Mathematics. Taught class from 2000-2002.

2. Taught “Vector Calculus” at University of Colorado-Boulder, Department of Applied Mathematics,

from 2002-2003.

## Publications

Ph.D. Thesis: *The Effect of Upper Level Features in The Atmosphere on Linear Theory and Linearized **Benjamin-Davis-Ono Theory for Internal Gravity Waves*, University of Michigan Press, Ann Arbor, 1999.

Peer-Reviewed Journal Articles:

- N. Flyer, Asymptotic upper bounds for the coefficients in the Chebyshev series expansion for a

general order integral of a function,*Mathematics of Computation*, 67, 1601-1616, 1998. - K. Kabin and N. Flyer, Reminiscences about difference schemes by Sergei Konstantinovich Godunov (translation from Russian),
*Journal of Computational Physics*, 153, 6-25, 1999. - J. P. Boyd and N. Flyer, Compatibility conditions for time-dependent partial differential equations and the rate of convergence of Chebyshev and Fourier spectral methods,
*Computer Methods in Applied Mechanics and Engineering,*175, 281-309, 1999. - N. Flyer and P. N. Swarztrauber, Convergence of spectral and finite difference methods for initial boundary value problems,
*SIAM Journal of Scientific Computing*, 23(5), 1731-1751, 2002. - N. Flyer and B. Fornberg, Accurate numerical solution of initial transients in convective-diffusive equations,
*Journal of Computational Physics*, 184(2), 526-539, 2003 - N. Flyer and B. Fornberg, On the nature of initial-boundary value solutions for dispersive equations,
*SIAM Journal of Applied Mathematics*, 64(2), 546-564, 2004. - N. Flyer, B. Fornberg, S. Thomas and B.C. Low, Magnetic field confinement in the solar corona. I.

Force-free fields,*The Astrophysical Journal*, 606, 1210-1222, 2004 - N. Flyer, B. Fornberg, S. Thomas and B.C. Low, Magnetic field confinement in the solar corona. II.

The weight of plasmas,*The Astrophysical Journal*, 631, 1239-1259, 2005 - B. Fornberg and N. Flyer, Accuracy of radial basis function interpolation and derivative

approximations in 1-D,*Advances in Computational Mathematics*, 23, 5-20, 2005. - M. Zhang, N. Flyer, B.C. Low, Magnetic field confinement in the corona: The role of magnetic

helicity accumulation, The Astrophysical Journal, 644(1), 575-586, 2006. - N. Flyer, Exact polynomial reproduction for oscillatory radial basis functions on infinite lattices,
*Computers and Mathematics with Applications*, 51(8), 1199-1208, 2006. - N. Flyer and G.B. Wright, Transport schemes on a sphere using radial basis functions,
*Journal of**Computational Physics*, 226, 1059-1084, 2007. - B.C. Low and N. Flyer, The topological nature of boundary value problems for force-free magnetic

field,*The Astrophysical Journal*, 668(1), 557-570, 2007. - B. Fornberg, N. Flyer, S. Hovde, C. Piret, Locality properties of radial basis function expansion

coefficients for equispaced interpolation,*IMA Journal of Numerical Analysis*, 28, 121-142, 2008. - A. Malmberg, A. Arellano, D. P Edwards, N. Flyer, D. Nychka, and C. K Wikle, Interpolating fields

of carbon monoxide data using a hybrid statistical-physical Model,*Annals of Applied Statistics*, 2(4),

1231-1248, 2008. - N. Flyer and A.S. Fokas, A new method for the numerical integration of evolutionary partial

differential equations. I. The half line,*Proc. Roy. Soc. A*, 464(2095), 1823-1849, 2008. - M. Zhang and N. Flyer, The dependence of the helicity bound of force-free magnetic fields on

boundary conditions,*The Astrophysical Journal*, 683(2), 1160–1167, 2008. - N. Flyer and G.B. Wright, A radial basis function method for the shallow water equations on a

sphere,*Proceedings of the Royal Society A*, 465, 1949-1976, 2009. - A.S. Fokas, N. Flyer, S.A. Smitherman, E. Spence, A semi-analytical numerical method for solving

evolution and elliptic partial differential equations,*J. Comput. Appl. Math.*, 227, 59-74, 2009. - K. Miller, B. Fornberg, N. Flyer, and B.C. Low, Magnetic relaxation of the solar corona,
*The**Astrophysical Journal*, 690, 720-733, 2009. - B. Fornberg, N. Flyer, and J.M. Russell, Comparisons between pseudospectral and radial basis

function derivative approximations,*IMA Journal of Numerical Analysis*, 30, 149-172, 2010. - N. Flyer and E. Lehto, Rotational transport on a sphere: Local node refinement with radial basis

functions,*Journal of Computational Physics*, 229, 1954-1969, 2010. - G.B. Wright, N. Flyer and D.A. Yuen, A hybrid radial basis function pseudospectral method for

thermal convection in a 3-D spherical shell,*Geophys., Geochem., Geosyst.*, 11,Q07003 2010. - N. Flyer and B. Fornberg, Radial basis functions: Developments and applications to planetary scale

flows,*Computers and Fluids*, 46, 23-32, 2011. - . B. Fornberg, E. Larsson, and N. Flyer, Stable computations with Gaussian radial functions ,
*SIAM J.**Sci. Comput.*, 33(2), 869-892, 2011. - Fornberg, B. and Flyer N., Some numerical tests on Laplace’s equation with the Fokas boundary

integral approach,*Proc Roy. Soc. A*, 467(2134), 2983-3003, 2011. - N. Flyer, Z. Qin, and R. Temam, A penalty method for numerically handling dispersive equations

with incompatible initial and boundary data,*Num. Meth. PDEs*, in press 2012. - N. Flyer, E. Lehto, S. Blaise, G. Wright, A. and St. Cyr, RBF-generated finite differences for

nonlinear transport on a sphere: shallow water simulations,*J. Comp. Phys.*, accepted, 2012. - M. Zhang, N. Flyer, and B.C. Low, Magnetic helicity of self-similar axisymmetric force-free fields,
*The Astrophysical Journal*, accepted, 2012. - E. Bollig, N. Flyer, and G. Erlebacher, Using radial basis function finite difference (RBF-FD) for PDE Solutions on the GPU,
*J. Comp. Phys.*, submitted, 2012.

### Book Chapters (Peer-Reviewed)

B. Fornberg and N. Flyer, The Gibbs Phenomenon for Radial Basis Functions, in *The Gibbs**Phenomenon in Various Representations and Applications* , ed. A. Jerri, Chapter 6, pp. 201-224, Sampling Publishing, Potsdam, NY, 2011.

Books Under Contract

B. Fornberg and N. Flyer, *Radial Basis Functions: Developments and Applications*, SIAM Press, Philadelphia, PA, due Summer 2012.

## **Invited Talks**

- “Radial basis functions: A new technique for solving PDEs ”, Dept. of Applied Mathematics, University of Colorado, Boulder, 2002.
- “Corner singularities for initial -boundary value problems - Illustration and remedy for convectivediffusive equations”, Department of Mathematics, Hong Kong Baptist University, March 2002.
- “Convergence of spectral and finite-difference methods for initial-boundary value problems”, Department of Mathematics, Hong Kong Baptist University, June 2002.
- “Accurate numerical resolution of transients for convection-diffusion equations”, Department of Scientific Computing, Uppsala University, Sweden, June 2002.
- “The elusive time-space corner singularity: The nature of initial-boundary value problems”, Korean Advanced Institute of Science and Technology (KAIST), Taegon, South Korea, March 2004.
- “Radial basis functions: The basics and why they are hot”, 12th Applied Math Forum of South Korea, March 2004, (Plenary speaker)
- “The elusive time-space corner singularity: The nature of initial-boundary value problems”, Department of Mathematics, Kyungpook National University, Daegu, South Korea, March 2004.
- “The elusive time-space corner singularity: The nature of initial-boundary value problems”, Colorado School of Mines, May 2004.
- “Applications of asymptotics to geophysical fluid dynamics”, Division of Scientific Computing, Uppsala University, Sweden, June 2005.
- “The nature of initial-boundary value problems and their ramifications on high order methods”, Department of Mathematics, University of Utah, Salt Lake City, January 2006.
- “Solving hyperbolic PDEs in spherical geometry with radial basis functions”, Korean SIAM Annual Meeting, Daegu, South Korea, May, 2006. (Plenary Speaker)

Conference Site and Presentation - “Transport schemes on a sphere using radial basis functions”, Division of Scientific Computing, Uppsala University, Sweden, June 2006.
- “Modeling simple atmospheric flows on a sphere using radial basis functions”, Department of Applied Math, University of Colorado, Boulder, April 2007.
- “The character of initial-boundary value problems and their numerical solution”, Wichita State University, Kansas, August 2007.
- “The character of initial-boundary value problems and their numerical solution”, University of Cambridge, Department of Applied Mathematics and Theoretical Physics, UK, September 2007.(Plenary speaker)
- “Geophysical modeling using radial basis functions”, Division of Scientific Computing, Uppsala University, Sweden, May 2008.
- “Geophysical modeling using radial basis functions”, Max Planck Institute for Plasma Physics,

Garching, Germany, June 2008. - “Moving vortices on a sphere: Local node refinement for radial basis functions”, SIAM Annual Meeting, San Diego, CA, July 2008.
- “A radial basis function shallow water model and local refinement”, Los Alamos, NM, Sept. 2008.
- “Geophysical modeling using radial basis functions”, University of Wyoming, October 2008.
- “Applications of radial basis functions to solid earth geophysics”, SANUM (South African Symposium on Numerical and Applied Mathematics), University of Stellenbosch, South Africa, April 2009 (Plenary speaker)
- “Applications of radial basis functions to modeling atmospheric flows”, Department of Atmospheric,

Oceanic, & Planetary Physics, University of Oxford, UK, May 2009. - “Radial basis functions methods for modeling atmospheric and solid earth flows”, Mathematical Institute, University of Oxford, UK, June 2009. http://www.maths.ox.ac.uk/node/9277
- “Modeling mantle convection in a 3-D spherical shell with a hybrid radial basis function method”, ENUMATH (European Conference on Numerical Mathematics and Advanced Applications), Uppsala University, Sweden, July 2009. http://www.enumath.eu/link/uppsala.html
- “Radial basis function methods for the geosciences”, Illinois Institute of Technology, October 2009.
- “The elusive time-space corner singularity: The hidden nature of initial-boundary value problems and

its impact on numerics”, University of Indiana, Bloomington, IN, October 2009. - “Radial basis function methods for geofluid modeling”, Institute for Mathematics and its Applications (IMA), University of Minnesota, Minneapolis-St. Paul, MN, April 2010 http://www.ima.umn.edu/videos/index.php?id=1224 (web – casted)
- “A hybrid analytical-numerical method for evolutionary PDEs”, International Centre for Mathematical Sciences (ICMS), Edinburgh, UK May 2010 (Plenary Speaker)
- “The Gibbs phenomenon for radial basis functions”, SIAM Annual Meeting, July 2010.
- “Recent developments in radial basis functions”, SIAM Annual Meeting, July 2010.
- “Resolving planetary-scale flows with radial basis functions”, SIAM Annual Meeting, July 2010.
- “The elusive time-space corner singularity: The hidden nature of initial-boundary value problems and its impact on numerics”, University of Kent, Oct. 2010
- “The hidden nature of initial-boundary value problems and its impact on numerics”, University of Oxford, UK, Oct. 2010
- “Radial basis function methods for computational geosciences”, Arizona State University April 2011

http://math.asu.edu/node/3333 - “Radial basis functions for computational geoscience”, Current challenges in climate modelling 2011,

Uppsala University, Sweden, May 26-27, 2011 (Plenary Speaker),http://www2.math.uu.se/cim/events/abstract_climate_Flyer.html - NSF/CBMS Regional Conference in the Mathematical Sciences-“Radial Basis Functions”, University

of Massachusetts-Dartmouth, Dept. of Mathematics, June 2011 (Principal Lecturer – 5 lectures, funded by grant from NSF) http://www.umassdcomputing.org/conference/rbfcbms2011/

**Research Interests**

**Research Interests****Radial Basis Functions (RBFs) for the Geosciences**

Advancing the understanding of the mathematical properties of RBFs and their potential for solving PDEs encountered in the solar and geosciences. Focuses on development of high-order RBF strategies that are benchmarked against large-scale community models and standard codes run at super-computing centers.

**Force-free fields in the Solar Corona**

Advancing the understanding of the mathematical properties of RBFs and their potential for solving PDEs encountered in the solar and geosciences. Focuses on development of high-order RBF strategies that are benchmarked against large-scale community models and standard codes run at super-computing centers.

**Numerical Methods for PDEs with Corner Singularities**

Describe and analyze the behavior of singularities that occur where the initial temporal and spatial domains meet (i.e. time-space corner singularities). Demonstrate the degradation of high-order numerical methods due to such singularities and devise correction strategies to restore accuracy, especially for spectral methods.

**Force-free fields in the Solar Corona**

Analytical and numerical approaches to study the properties of self-confinement for nonlinear force-free fields. Development of numerical solvers for highly elliptic PDEs whose solutions are multiple valued in parameter space. Free-boundary solvers and investigation of the mathematical nature of these PDEs in 3D.