# Donald A French

## Professor

### French Hall

4411

A&S Mathematical Sciences Adjuncts - 0025

## Education

PhD, Cornell University Ithaca, NY, 1985 (Applied Mathematics)

MS, Cornell University Ithaca, NY, 1983 (Applied Mathematics)

BA (Double Major), State University of New York Oswego, NY, 1980 (Mathematics and Physics)

## Positions and Work Experience

1985 -1987 Research Assistant Professor, Purdue University, Lafayette, IN

1987 -1990 Assistant Professor, Carnegie Mellon University, Pittsburgh, PA

1990 -1993 Assistant Professor, University of Cincinnati, Cincinnati, OH

1993 -1999 Associate Professor, University of Cincinnati, Cincinnati, OH

1999 -To Present Full Professor , University of Cincinnati, Cincinnati, OH

2010 -To Present Contractor/Consultant, Wright Patterson Air Force Base, Dayton, OH

2015 -2017 Graduate Program Director, University of Cincinnati,

1999 -2001 Graduate Program Director,

## Research and Practice Interests

Recent work has been interdisciplinary and focussed on mathematical modeling in Cellular Physiology with emphasis on problems in Neuroscience. Have worked on inverse problems involving olfactory cilia with Steve Kleene (College of Medicine) since 2001. Have also studied neuronal & social networks as well as biofilms.

Research between 1985 and 2001 was on error analysis for finite element methods for partial differential equations and primarily time-dependent problems arising in applications such as phase transitions, viscoelasticity, and thermoelasticity. Investigations into the development of time discretizations using finite element techniques have led to various energy preserving schemes. Have recently returned to analysis of meshfree and dG methods.

## Research Support

Grant: #DMS-0515989 Investigators:French, Donald 07-01-2005 -08-31-2009 National Science Foundation Identification of Ion Channel Distributions in Olfactory Cilia by Mathematical Modeling Role:PI $168,638.00 Closed Level:Federal

Grant: #DMS-0207145-001-REU Investigators:French, Donald 09-01-2002 -08-31-2004 National Science Foundation Career Development in Mathematical Physiology Role:PI $100,000.00 Closed Level:Federal

## Abbreviated Publications

### Other Publication

French, Donald (1992). Analysis and computation of solutions to an evolution problem in nonlinear viscoelasticity. *Proceedings of the Ninth Army Conference on Applied Mathematics and Computing*, *92-1*, 107-113.

French, Donald (1993). Long time behavior of a numerical approximation to a nonlinear evolution problem in viscoelasticity. *Proceedings of the Tenth Army Conference on Applied Mathematics and Computing*, *93-1*, 23-28.

French, Donald (1994). Analysis and computation of approximate solutions to a simple model of shear band formation in one and two dimensions. *Proceedings of the Eleventh Army Conference on Applied Mathematics and Computing*, *94-1*, 287-298.

Abbot, J.S., French, Donald, & et al. (1995). Determining index data and refracted/diffracted rays. *Proceedings of the Eleventh Workshop on Mathematical Problems in Industry, Los Alamos National Laboratory Technical Report LA-UR 95-4038*.

Hendricks, F. et al. (1997). The design of hard drive slider bearings. *Proceedings of the Twelfth Workshop on Mathematical Problems in Industry* 47-60.

Hector, Jr., L.G. et al. (1999). Thermomechanical models of air gap nucleation during pure metal solidification on moving molds with periodic surface topographies. *Proceedings of the Fourteenth Workshop on Mathematical Problems in Industry*.

Mauk, M. et al. (2000). A mathematical model for epitaxial semiconductor crystal growth from a vapor phase masked substrate. *Proceedings of the Fifteenth Workshop on Mathematical Problems in Industry*.

D.A. French, M. C. Galbraith and M. Osorio, Error Analysis of a Modified Discontinuous Galerkin Recovery Scheme for Diffusion Problems, AIAA Paper 2010-1071, Jan. 2010.

D.A. French and C.W. Groetsch, Olfactory cilia: a case study in inverse modeling, Proceedings of First, Symposium on Inverse Problems and Applications, Ixtapa, Mexico, September 2010.

### Peer Reviewed Publications

Badamdorj, Dorjsuren, Edwards, David A, French, Donald A, & Kleene, Steven J (2008). Identification of Cl(Ca) channel distributions in olfactory cilia. *Mathematical methods in the applied sciences*, *31*(15), 1860-1873.

French, Donald A, & Edwards, David A (2007). Perturbation approximation of solutions of a nonlinear inverse problem arising in olfaction experimentation. *Journal of mathematical biology*, *55*(5-6), 745-65.

French, D A, & Gruenstein, E I (2006). An integrate-and-fire model for synchronized bursting in a network of cultured cortical neurons. *Journal of computational neuroscience*, *21*(3), 227-41.

Flannery, Richard J, French, Donald A, & Kleene, Steven J (2006). Clustering of cyclic-nucleotide-gated channels in olfactory cilia. *Biophysical journal*, *91*(1), 179-88.

French, Donald A, Flannery, Richard J, Groetsch, Charles W, Krantz, Willam B, & Kleene, Steven J (2006). Numerical Approximation of Solutions of a Nonlinear Inverse Problem Arising in Olfaction Experimentation. *Mathematical and computer modelling*, *43*(7-8), 945-956.

Badamdorj, D., French, D.A. and Kleene S. (2010), Clustering of Cl(Ca) ion channels in the cilia of frog olfactory receptor neurons. PLoS ONE 5.

D.A. French, M. C. Galbraith and M. Osorio, Error Analysis of a Modified Discontinuous Galerkin Recovery Scheme for Diffusion Problems, Applied Mathematics and Computation, 218 (2012), 7144-7154.

D.A. French and M. Osorio, Error Estimates for an Element Free Galerkin Method with Diffuse Derivatives and Penalty Stabilization, Computational Mechanics, 50 (2012), 657-664

French, D.A., & Groetsch, C. (2007). Numerical Approximation of Solutions of a Constrained Integral Equation Arising in Olfaction Experimentation. *J. of Physics: Conference Series*, *73*, 1-10.

French, D.A., & Edwards, D. (2007). Perturbation derivation of ligand-gated ion channel distributions arising in olfaction experimentation. *J. Math. Biology*, *55*, 745-765.

D.A. French and C.W. Groetsch, Numerical solution of a class of integral equations arising in a biological laboratory procedure, Integral Methods in Science and Engineering, Vol. 2, Computational Methods, C. Constanda and E. Perez, Eds. Birkauser, Boston (2010), ISBN 978-0-8176-4896-1.

R. Braun, D.A. French, Z. Teymuorglu and T. Lewis (2010).

Continuum models of the spread of alcoholism, Journal of Integral Equations and Applications, 22, 441-462.French, Donald, Larsson, S., & Nochetto, R. (2001). A posteriori error estimates for a finite element approximation of the obstacle problem in L1. *Computational Methods in Applied Mathematics*, *1*, 18-38.

Albert, S., Cockburn, B., French, Donald, & Peterson, T. (2001). A posteriori error estimates for general numerical methods for the Hamilton-Jacobi equation. *Math. Comp.*, *71*, 49-76.

Copetti, M.I.M., & French, Donald (2003). Numerical solution of a thermoviscoelastic contact problem by a penalty method. *SIAM J. Num. Anal.*, *41*, 1487-1504.

French, Donald (2003). Analysis of the convergence behavior of the localized nonlinear approximation for electromagnetic scattering. *J. Comp. Appl. Math.*, *161*, 27-39.

Copetti, M.I.N., & French, Donald (2004). Numerical studies of thermoelastic contact problem. *Applied Mathematica lModeling*, *28*, 323-332.

French, Donald (2004). Identification of a free energy functional in an integro-differential equation model for neuronal activity. *Appl. Math. Lett.*, *17*, 1047-1051.

Copetti, M.I.M., & French, Donald (2005). A posteriori error estimates for low order continuous and discontinuous Galerkin methods for a thermoelastic contact problem. *Appl. Num. Math.*, *55*, 439-457.

French, Donald, & Oh, J. (2006). Error Analysis of a Specialized Numerical Method for Differential Equation Models in Neuroscience. *Appl. Math. Comput.*, *172*, 491-507.

Flannery, R., French, Donald, Groetsch, C., Krantz, W., & Kleene, S. (2006). Identification of CNG channel distributions in frog olfactory cilia. *Math. Comp. Modelling*, *43*, 945-956.

Flannery, R., French, Donald, & Kleene, S.J. (2006). Clustering of CNG channels in the cilia of frog olfactory receptor neurons. *Biophys. J.*, *91*, 179-188.

French, Donald, & Gruenstein, E. (2006). An Integrate-and-Fire Model for Synchronized Bursting in a Network of Cultured Cortical Neurons. *J. Comp. Neurosci*, *21*, 227-241.

D.A. French and M. Osorio, A Galerkin Meshfree method with Diffuse Derivatives and Stabilization: Two Dimensional Case, Revista Ingenieria Y Ciencia (J. Engr. Sci.), 9 (2013), 53-76 (In connection with the VIII Colombian Meeting on Numerical Methods.).

J. Clack, D.A. French and Mauricio Osorio, Analysis of Pseudo-Derivative MLS Schemes for Fractional Derivative Problems, Projections Journal of Mathematics, 36 (2017), 435-448.

Hailong Li, Kristen Fox-Neff, D.A. French, Benjamin Vaughan, Jerzy Szaflarski and Yu Li, Parallel EPI artifact correction (PEAC) for N/2 ghost suppression in neuroimaging applications, In Press -- Magnetic Resonance Imaging, (2013), 7 pages.

Overset Methods and Robin Boundary Conditions (with J.A. Benek, C. Schrock and M. Galbraith)

Comparison between Discontinuous Galerkin Method and Cohesive Element Method On the Convergence and Dynamic Wave Propagation Issue (with Wenlong Zhang and Ala Tabiei), International Journal for Computational Methods in Engineering and Applied Science.

PDE based trajectory planning for multiple unmanned air vehicles in dynamic and uncertain environments (with M. Radmanesh and M. Kumar -- To appear in Journal of Dynamic Systems, Measurement and Control)

Analysis of an Individual-Based Network Model for the Spread of Alcohol Abuse (with M. Eisenberg and T. Nance), J. Biological Dynamics}, 12 (2018), 509-526.

### Work in Progress

D.A. French and T.J. Lewis, Analysis of Neurons Pairs Coupled by Voltage Dependent Gap Junctions

N. Cogan, D.A. French, M. Kupferle, B. Vaughan and S. Lim, Biofilms in Urban Water Distribution Systems and their Impact on Health (Submitted to Mathematical Methods in the Applied Sciences).

D.A. French, K. Fox-Neff, Yu Li, B. Vaughan, Inverse Problems arising in MRI Analysis of HIFU Ablation of Cancer

D.A. French, S. Toprakseven, D. Qian and B. Vaughan, XFEM Discontinuous Galerkin Schemes for Singular Problems

D.A. French, Scaling up Agent-Based Models of Partial Differential Equations

### Peer Reviewed Conference/Workshop Proceedings

D.A. French, M.C. Galbraith and J.A. Benek, Analysis of Chimera Schemes with Schwarz Iteration, AIAA Conference Paper (January 2014 Conference).

D.A. French, C. Schrock and J.A. Benek, Direct Overset Finite Element Methods for Aerospace Problems, AIAA Aviation June 2016.

D.A. French, J.A. Benek and C. Schrock, Least Squares Overset Finite Element Method: Error Analysis on a Prototype Aerospace Problem (AIAA Aviation 2017)

A Partition of Unity Finite Element Method for Overset Problems (with J.A. Benek and C. Schrock), AIAA Aviation June 2018.

## Presentations

### Invited Presentations

D.A. French
(06-2000. )
*The evaluation of option prices on baskets via a perturbation approach *.Mathematical Problems in Industry Workshop, University of Delaware.

D.A. French
(11-2000. )
*Time discretizations for evolution problems derived with finite element techniques *.Seminar, University of Kentucky.

D.A. French
(05-2005. )
*Numerical approximation of solutions of a nonlinear inverse problem arising in olfaction experimentation *.Midwest Numerical Analysis Conference, University of Iowa.

D.A. French
(07-2005. )
*Numerical approximation of solutions of a nonlinear inverse problem arising in olfaction experimentation *.SIAM Annual Meeting, New Orleans, LA.

D.A. French
(10-2005. )
*Numerical approximation of solutions of a nonlinear inverse problem arising in olfaction experimentation *.Colloquium, Uinversity of Delaware.

D.A. French
(04-2006. )

D.A. French
(07-2006. )
*Identification of ion channel distributions in olfactory cilia *.SIAM Annual Meeting, Raleigh, NC.

D.A. French
(10-2006. )
*Identification of ion channel distributions in olfactory cilia *.AMS Sectional Meeting, Cincinnati, OH.

D.A. French
(04-2007. )
*Weak Coupling Analysis of Rectifying Gap Junctions *.Seminar, University of California, Davis.

D.A. French
(07-2007. )
*Identification of ion channel distributions in olfactory cilia *.International Conference, Zurich, CH.

D.A. French
(04-2008. )
*Identification of ion channel distributions in olfactory cilia *.Indiana University Purdue University at Indianapolis.

D.A. French
(10-2008. )
*On an integro-differential equation model for the spread of alcoholism *.Department Seminar, University of Cincinnati.

D.A. French
(10-2009. )
*On Chen's mathematical model of biofilm growth *.Taft Research Seminar,

D.A. French
(03-2010. )
*Identification of ion channel distributions in olfactory cilia *.Lecture, University of Maryland, Baltimore County.
Level:National

D.A. French
(05-2010. )
*Error Analysis of Meshfree and Discontinuous Galerkin Methods *.Lecture, Mechanical Engineering, University of Cincinnati.
Level:Local

D.A. French
(09-2010. )
*From the Numerical Analysis Bench: DG for Elliptic Problems *.Contractor Lecture, Wright-Patterson Air Force Base.
Level:State

D.A. French
(11-2010. )
*Analysis of Moving Least Square Meshfree Methods with Diffuse Derivatives and Penalty Stabilization *.Finite Element Circus, University of Minnesota.
Level:National

Donald French
(11-2010. )
*From the Numerical Analysis Bench: Discontinuous Galerkin Methods *.Colloquium, University of Kentucky Mathematics Department.
Level:University

D.A. French
(06-2011. )
*Numerical approximation of solutions of a nonlinear inverse problem arising in olfaction *.Conference in honor of C.M. Elliott's 60th Birthday, Warwick, UK. Conference. .
Level:International

D.A. French
(09-2011. )
*From the Numerical Analysis Bench: Discontinuous Galerkin Methods *.Contractor Lectures, Wright-Patterson Air Force Base.
Level:State

D.A. French
(02-2012. )
*Mathematical Biosciences at University of Cincinnati *.Institute Partners Meeting, Ohio State University . Other Institution. .
Level:State

D.A. French
(05-2012. )
*Analysis of Individual-Based Network Models *.Taft Annual Symposium, University of Cincinnati. UC. .
Level:University

D.A. French
(07-2012. )
*Analysis of a Stabilized Meshfree Method *.Multiscale Methods Workshop, Northwestern University, Evanston, IL. Conference. .
Level:International

D.A. French
(09-2012. )
*From the Numerical Analysis Bench: DG and Spectral Methods for Conservation Laws *.Contractor Talk, Wright Patterson Base, Dayton, OH. Other Institution. .
Level:National

D.A. French
(11-2012. )
*Inverse Problems in the Biomedical Sciences *.BME 7001 Class, University of Cincinnati.
Level:University

D.A. French
(09-2013. )
*Chimera Schemes and Localization Techniques *.Wright-Patterson Air Force Base.
Level:State

D.A. French
(04-2013. )
*Modeling the Spread of Alcohol Abuse *.Tennessee State University.
Level:National

D.A. French
(11-2013. )
*Inverse Problems in the Biosciences *.BME 7001 Invited Presentation, University of Cincinnati.
Level:University

(08-28-2014. )
*From the Numerical Analysis Bench: Galerkin Overset Methods *.Invited Presentation, Wright Patterson Air Force Base.
Level:National

(04-25-2015. )
*Error Analyses of Stabilized Pseudo-Derivative Methods *.Numerical Analysis Day, Wright State University. Conference. .
Level:National

(05-19-2015. )
*From the Numerical Analysis Bench: Finite Element Overset Methods *.CCAS Review, Tec-Edge Dayton, OH. Professional Meeting. .
Level:National

(12-17-2015. )
*From the Numerical Analysis Bench: Finite Element Overset Methods *.WPAFB. Other Institution. .
Level:State

(05-17-2016. )
*From the Numerical Analysis Bench: Overset Finite Element Methods *.CCAS Review, Ohio State University.
Level:National

(06-13-2016. )
*Theoretical Analysis of Direct Overset Finite Element Methods *.AIAA Aviation , Washington DC.
Level:International

D.A. French *The spread of alcohol abuse on network and a Schelling model IDE model *.Seminar, UC. .
Level:Department

D.A. French
(04-2017. )
*From the Numerical Analysis Bench: Error Analysis of Overset Finite Element Methods *.CCAS Review , Wright-Patterson AFB. Conference. .
Level:National

D.A. French
(06-2017. )
*Theoretical Error Analysis of Direct Overset Finite Element Methods *.AIAA Aviation, Conference. .
Level:National

D.A. French
(05-23-2018. )
(In Press. )
*From the Numerical Analysis Bench: Error Analysis of Finite Element Overset Methods *.CCAS Review, Ohio State University. Conference. .
Level:National

D.A. French
(06-26-2018. )
(In Press. )
*Theoretical Error Analysis of Partition of Unity Overset Finite Element Methods *. AIAA Aviation, Atlanta GA. Conference. .
Level:International

D.A. French
(12-07-2018. )
(In Press. )
*Error Analyses of Stabilized Pseudo-Derivative MLS Methods *.Applied Mathematics Seminar, University of Cincinnati. UC. .
Level:Department

D.A. French
(In Press. )
*Overset Methods and Robin Boundary Condtions *. AIAA Aviation, Dallas TX.
Level:National

## Honors and Awards

06-1987 -07-1988 Numerical analysis of the Cahn-Hilliard equation. NSF Status:Recipient Level:National Type:Grant

06-1988 -06-1989 Finite element methods for nonlinear partial differential equations NSF Status:Recipient Level:National Type:Grant

07-1990 -09-1992 Numerical solution of nonlinear evolution equations in applied problems ARO Status:Recipient Level:National Type:Contract

09-2002 -09-2003 Career Development in Mathematical Physiology NSF Status:Recipient Level:National Type:Grant

09-2004 -09-2005 Mathematical Modeling of Olfactory Cilia (with S. Kleene) URC Status:Recipient Level:University Type:Grant

09-2005 -09-2009 Identification of Ion Channel Distributions in Olfactory Cilia (with S. Kleene) NSF Status:Recipient Level:National Type:Grant

09-2009 -09-2010 Simulation of the Oscillations in a Cluster of Neurons in a Neuronal Network (with C.C. Ho, E. Gruenstein and A. Minai.) URC Status:Recipient Level:University Type:Grant

06-2011 -06-2012 Mathematical Modeling of Biofilms in Urban Pipes (with M. Kupferle, S. Lim, B. Vaughan and D. Hassett) University Research Council Status:Recipient Level:University Type:Fellowship

09-2011 -09-2012 Mathematical and Computational Study of Problems arising in the Social Biological and Applied Sciences Taft Fund Status:Recipient Level:University Type:Fellowship

09-2011 -09-2012 Taft Center Fellow Taft Fund Level:University

## Service

Graduate Program Director Type:Departmental Service Level:Department 1999 -2001

Mathematical Sciences (Executive ) Type:Departmental Service 01-2012 -06-2012

Mathematical Sciences (RPT ) Committee Member Type:Departmental Service 09-2011 -09-2012

Mathematical Sciences (Graduate Advising ) Type:Departmental Service 09-2011 -09-2012

(Undergraduate Capstone for Colin Craig ) Mentor Type:Departmental Service

Mathematical Sciences (Re-Organization ) Type:Departmental Service

(Taft Executive ) Type:University/College Service

(Taft Center Fellows Evaluation ) Type:University/College Service

(PhD Student ) Committee Member Type:Departmental Service

(MS Oral Examination ) Committee Member Type:Departmental Service

Type:University/College Service

Mathematical Sciences (Graduate Student Executive Committee ) Committee Member 09-2012 -06-2012

(Graduate Affairs Committee ) Member Type:Departmental Service

(Executive Committee ) Member Type:Departmental Service

(Taft Executive Committee ) Member Type:University/College Service

(Taft Center Fellows Committee ) Committee Chair Type:University/College Service

(Graduate Student Executive Committee ) Member Type:Departmental Service

(Graduate Affairs Committee ) Type:Departmental Service Level:Department 01-01-2014 -12-31-2014

Taft Fund (Executive Committee ) Member Type:University/College Service Level:College 01-01-2014 -12-31-2014

(Hiring Committee ) Committee Chair Type:Departmental Service 12-01-2014 -03-31-2015

(Graduate Affairs Committee ) Committee Chair Type:Departmental Service Level:University 08-2015 -08-2017

(Master Oral Examination ) Committee Chair Type:Departmental Service Level:University

(PhD Dissertation Committee ) Member Type:Departmental Service Level:University

(RPT ) Member Type:Departmental Service

(Graduate Program Director ) Type:Departmental Service 08-2015 -08-2017

(Graduate Student Executive Committee ) Committee Chair Type:Departmental Service 08-2015 -08-2017

AIAA Aviation (Refereed Six Abstracts for 2017 Conference. ) Reviewer Type:Service to Professional Associations Level:National

(Graduate Program Review & Site Visit. ) Committee Chair Type:Departmental Service Level:University

(Diversity Hiring - Kamal Barley ) Committee Chair Type:Departmental Service

(Graduate Affairs Committee ) Committee Chair Type:Departmental Service 08-2015 -08-2017

Math Modeling and Numerical Analysis Peer Review/Referee Type:Service to Professional Associations Level:International

(Graduate Student Executive Committee (GSEC) ) Member Type:Departmental Service Level:Department

(RPT ) Member Type:Departmental Service Level:Department 08-25-2016 -08-25-2018

## Keywords

Mathematical bioscience; numerical analysis; scientific computation

## Professional Affiliation

04-01-2010 -To Present: Contractor at Wright Patterson AFB (2010-Present).

## Courses Taught

Applied Linear Algebra Level:Graduate

Numerical Analysis

Numerical Analysis Level:Graduate

Advanced Numerical Analysis Level:Graduate

Calculus II

PDE & Fourier Analysis Level:Graduate

Numerical Analysis Level:Graduate

Mathematics of Social Choice Level:Undergraduate

Mathematics for Social Choice Level:Undergraduate

PDE & FA Level:Both

Numerical Analysis Level:Graduate

Advanced Numerical Analysis Level:Graduate

Numerical Analysis Level:Graduate

Numerical Analysis Level:Graduate

Math Modeling Level:Undergraduate

PDE and Fourier Analysis Level:Both

Advanced Numerical Analysis Level:Graduate

Dynamical Systems Level:Undergraduate

Numerical Analysis Level:Both

PDE and Fourier Analysis Level:Both

## Faculty Development Activities

1992 Numerical Methods in Applied Mathematics 15-MATH-561-001 - Created new quarter class., Type:Other

1997 Applied Mathematics Practicum 15-MATH-517-001 -- Created new quarter class., Type:Other

2009 Mathematical Biology (Undergraduate) 15-MATH-378-001 -- Created new quarter class., Type:Other

2009 Mathematical Biology (Graduate) 15-MATH-562-001 -- Created new quarter course., Type:Other