Mark Ainsworth obtained his PhD in Mathematics at Durham University in the United Kingdom. Prior to moving to Brown, he held the 1825 Chair in Mathematics at Strathclyde University and was Director of
NAIS , a joint centre between the Universities of Edinburgh, Heriot-Watt and Strathclyde, and Edinburgh Parallel Computing Centre to develop UK capacity in high performance computing and numerical analysis.
Ainsworth, Mark, Davydov, Oleg, Schumaker, Larry L. Bernstein-Bézier finite elements on tetrahedral–hexahedral–pyramidal partitions. Computer Methods in Applied Mechanics and Engineering/Computer Methods in Applied Mechanics and Engineering. 2016; 304 : 140-170. |
Zayernouri, Mohsen, Ainsworth, Mark, Karniadakis, George Em A unified Petrov–Galerkin spectral method for fractional PDEs. Computer Methods in Applied Mechanics and Engineering/Computer Methods in Applied Mechanics and Engineering. 2015; 283 : 1545-1569. |
Ainsworth, Mark, Barrenechea, Gabriel R., Wachtel, Andreas Stabilization of High Aspect Ratio Mixed Finite Elements for Incompressible Flow. SIAM J. Numer. Anal./SIAM Journal on Numerical Analysis. 2015; 53 (2) : 1107-1120. |
Ainsworth, Mark, Andriamaro, Gaelle, Davydov, Oleg A Bernstein–Bézier Basis for Arbitrary Order Raviart–Thomas Finite Elements. Constr Approx/Constr Approx. 2014; 41 (1) : 1-22. |
Ainsworth, Mark Dispersive behaviour of high order finite element schemes for the one-way wave equation. Journal of Computational Physics/Journal of Computational Physics. 2014; 259 : 1-10. |
Ainsworth, Mark Pyramid Algorithms for Bernstein--Bézier Finite Elements of High, Nonuniform Order in Any Dimension. SIAM J. Sci. Comput./SIAM J. Sci. Comput.. 2014; 36 (2) : A543-A569. |
Ainsworth, Mark, Vejchodský, Tomáš Robust error bounds for finite element approximation of reaction–diffusion problems with non-constant reaction coefficient in arbitrary space dimension. Computer Methods in Applied Mechanics and Engineering/Computer Methods in Applied Mechanics and Engineering. 2014; 281 : 184-199. |
Ainsworth, Mark, Allendes, Alejandro, Barrenechea, Gabriel R., Rankin, Richard Fully computable a posteriori error bounds for stabilised FEM approximations of convection-reaction-diffusion problems in three dimensions. International Journal for Numerical Methods in Fluids/International Journal for Numerical Methods in Fluids. 2013; : n/a-n/a. |
Ainsworth, Mark, Allendes, Alejandro, Barrenechea, Gabriel R., Rankin, Richard On the Adaptive Selection of the Parameter in Stabilized Finite Element Approximations. SIAM Journal on Numerical Analysis/SIAM Journal on Numerical Analysis. 2013; 51 (3) : 1585-1609. |
Ainsworth, Mark, Rankin, Richard Guaranteed computable bounds on quantities of interest in finite element computations. International Journal for Numerical Methods in Engineering/International Journal for Numerical Methods in Engineering. 2012; 89 (13) : 1605-1634. |
Ainsworth, Mark, Ma, Xinhui Non-uniform order mixed FEM approximation: Implementation, post-processing, computable error bound and adaptivity. Journal of Computational Physics/Journal of Computational Physics. 2012; 231 (2) : 436-453. |
Ainsworth, Mark, Andriamaro, Gaelle, Davydov, Oleg Bernstein–Bézier Finite Elements of Arbitrary Order and Optimal Assembly Procedures. SIAM J. Sci. Comput./SIAM J. Sci. Comput.. 2011; 33 (6) : 3087-3109. |
Ainsworth, M., Allendes, A., Barrenechea, G. R., Rankin, R. Computable error bounds for nonconforming Fortin-Soulie finite element approximation of the Stokes problem. IMA Journal of Numerical Analysis/IMA Journal of Numerical Analysis. 2011; 32 (2) : 417-447. |
Ainsworth, Mark, Vejchodský, Tomáš Fully computable robust a posteriori error bounds for singularly perturbed reaction–diffusion problems. Numer. Math./Numer. Math.. 2011; 119 (2) : 219-243. |
Ainsworth, Mark, Rankin, Richard Realistic computable error bounds for three dimensional finite element analyses in linear elasticity. Computer Methods in Applied Mechanics and Engineering/Computer Methods in Applied Mechanics and Engineering. 2011; 200 (21-22) : 1909-1926. |
Ainsworth, Mark, Rankin, Richard Technical Note: A note on the selection of the penalty parameter for discontinuous Galerkin finite element schemes. Numer. Methods Partial Differential Eq./Numer. Methods Partial Differential Eq.. 2011; 28 (3) : 1099-1104. |
Ainsworth, Mark A framework for obtaining guaranteed error bounds for finite element approximations. Journal of Computational and Applied Mathematics/Journal of Computational and Applied Mathematics. 2010; 234 (9) : 2618-2632. |
Ainsworth, Mark, Rankin, Richard Fully Computable Error Bounds for Discontinuous Galerkin Finite Element Approximations on Meshes with an Arbitrary Number of Levels of Hanging Nodes. SIAM Journal on Numerical Analysis/SIAM Journal on Numerical Analysis. 2010; 47 (6) : 4112-4141. |
Ainsworth, Mark, Wajid, Hafiz Abdul Optimally Blended Spectral-Finite Element Scheme for Wave Propagation and NonStandard Reduced Integration. SIAM Journal on Numerical Analysis/SIAM Journal on Numerical Analysis. 2010; 48 (1) : 346-371. |
Mihai, L. Angela, Ainsworth, Mark A finite element procedure for rigorous numerical enclosures on the limit load in the analysis of multibody structures. Computer Methods in Applied Mechanics and Engineering/Computer Methods in Applied Mechanics and Engineering. 2009; 199 (1-4) : 48-60. |
Ainsworth, Mark, Mihai, L. Angela An adaptive multi-scale approach to the modelling of masonry structures. International Journal for Numerical Methods in Engineering/International Journal for Numerical Methods in Engineering. 2009; 78 (10) : 1135-1163. |
Mihai, L.A., Ainsworth, Mark An adaptive multi-scale computational modelling of Clare College Bridge. Computer Methods in Applied Mechanics and Engineering/Computer Methods in Applied Mechanics and Engineering. 2009; 198 (21-26) : 1839-1847. |
Ainsworth, M., Rankin, R. Constant free error bounds for nonuniform order discontinuous Galerkin finite-element approximation on locally refined meshes with hanging nodes. IMA Journal of Numerical Analysis/IMA Journal of Numerical Analysis. 2009; 31 (1) : 254-280. |
Ainsworth, Mark, Wajid, Hafiz Abdul Dispersive and Dissipative Behavior of the Spectral Element Method. SIAM Journal on Numerical Analysis/SIAM Journal on Numerical Analysis. 2009; 47 (5) : 3910-3937. |
Ainsworth, Mark, Demkowicz, Leszek Explicit polynomial preserving trace liftings on a triangle. Mathematische Nachrichten/Mathematische Nachrichten. 2009; 282 (5) : 640-658. |
Ainsworth, Mark, Rankin, Richard Guaranteed computable error bounds for conforming and nonconforming finite element analyses in planar elasticity. International Journal for Numerical Methods in Engineering/International Journal for Numerical Methods in Engineering. 2009; 82 (9) : 1114-1157. |
Ainsworth, Mark A Posteriori Error Estimation for Lowest Order Raviart–Thomas Mixed Finite Elements. SIAM J. Sci. Comput./SIAM J. Sci. Comput.. 2008; 30 (1) : 189-204. |
Ainsworth, Mark, Rankin, Richard Fully Computable Bounds for the Error in Nonconforming Finite Element Approximations of Arbitrary Order on Triangular Elements. SIAM Journal on Numerical Analysis/SIAM Journal on Numerical Analysis. 2008; 46 (6) : 3207-3232. |
Ainsworth, Mark, Rankin, Richard Robust a posteriori error estimation for the nonconforming Fortin--Soulie finite element approximation. Mathematics of Computation/Mathematics of Computation. 2008; 77 (264) : 1917-1939. |
Ainsworth, Mark A Posteriori Error Estimation for Discontinuous Galerkin Finite Element Approximation. SIAM Journal on Numerical Analysis/SIAM Journal on Numerical Analysis. 2007; 45 (4) : 1777-1798. |
Ainsworth, Mark, Demkowicz, Leszek, Kim, Chang-Wan Analysis of the equilibrated residual method for a posteriori error estimation on meshes with hanging nodes. Computer Methods in Applied Mechanics and Engineering/Computer Methods in Applied Mechanics and Engineering. 2007; 196 (37-40) : 3493-3507. |
Ainsworth, Mark, Mihai, L. Angela Modeling and numerical analysis of masonry structures. Numer. Methods Partial Differential Eq./Numer. Methods Partial Differential Eq.. 2007; 23 (4) : 798-816. |
Ainsworth, Mark, Mihai, L. Angela A comparison of solvers for linear complementarity problems arising from large-scale masonry structures. Appl Math/Appl Math. 2006; 51 (2) : 93-128. |
Ainsworth, M., Monk, P., Muniz, W. Dispersive and Dissipative Properties of Discontinuous Galerkin Finite Element Methods for the Second-Order Wave Equation. J Sci Comput/J Sci Comput. 2006; 27 (1-3) : 5-40. |
Ainsworth, Mark, Carstensen, Carsten, Dörfler, Willy Mini-Workshop: Convergence of Adaptive Algorithms. Oberwolfach Rep./Oberwolfach Rep.. 2005; : 2091-2138. |
Dörfler, W., Ainsworth, M. Reliable a posteriori error control for nonconforming finite element approximation of Stokes flow. Mathematics of Computation/Mathematics of Computation. 2005; 74 (252) : 1599-1620. |
Ainsworth, Mark Robust A Posteriori Error Estimation for Nonconforming Finite Element Approximation. SIAM Journal on Numerical Analysis/SIAM Journal on Numerical Analysis. 2005; 42 (6) : 2320-2341. |
Ainsworth, Mark Discrete Dispersion Relation for hp -Version Finite Element Approximation at High Wave Number . SIAM Journal on Numerical Analysis/SIAM Journal on Numerical Analysis. 2004; 42 (2) : 553-575. |
Ainsworth, Mark Dispersive and dissipative behaviour of high order discontinuous Galerkin finite element methods. Journal of Computational Physics/Journal of Computational Physics. 2004; 198 (1) : 106-130. |
Ainsworth, M. Dispersive properties of high-order Nedelec/edge element approximation of the time-harmonic Maxwell equations. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences/Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences. 2004; 362 (1816) : 471-491. |
Ainsworth, Mark, McLean, Bill, Tran, Thanh Diagonal scaling of stiffness matrices in the Galerkin boundary element method. The ANZIAM Journal/The ANZIAM Journal. 2000; 42 (01) : 141. |
2015 ARO MURI: Fractional PDEs for Conservation Laws and Beyond: Theory, Numerics and Applications
(Co-PI). October 2015-October 2020.
2015 ASCR SIRIUS: Science Driven Data Management for Multi-tiered Storage (Co-PI).
2013- UT Batelle Joint Faculty Appointment ORNL (PI).
2012 AFOSR Methods for High-order Multi-Scale and Stochastic Problems: Analysis, Algorithms, and Applications (Co-Investigator). 7/15/12-7/14/16.
2011 EPSRC EP/J007242/1 Optimal Design of Drug Eluting Stents (Co-PI).
2009 EPSRC EP/G036136/1 Numerical Algorithms and Intelligent Software for the Evolving HPC Platform
(Principal Investigator at Strathclyde). £4,550,814 plus additional contribution from Scottish
Funding Council. This is a collaborative award with Universities of Edinburgh, Heriot-Watt, and
Edinburgh Parallel Computer Centre (UK’s national supercomputer HeCTOR).
2008 EPSRC/Strathclyde RAIS Award Assessing and Quantifying the Accuracy of FEA of Thin-Walled Structures (Principal Investigator). Plus contribution from industrial partner, Ideas Ltd, Glasgow.
2007 EPSRC EP/E040993/1 Adaptive Numerical Methods for Optoelectronic Devices. (Principal Investigator).
2007 Hewlett-Packard Laboratories, UK. Adaptive Numerical Methods for Optoelectronic Devices. (Principal
Investigator).
2005 Royal Society of Edinburgh/Scottish Executive Research Fellowship. (Principal Investigator). Provides
funds for appointment of lecturer to release recipient from all academic duties for one year.
2003 EPSRC GR/S10153/01 Multiscale Modelling and Numerical Analysis of Masonry. (Principal Investigator).
2003 Leverhulme Trust Fellowship Robust Algorithms in Computational PDEs. (Principal Investigator).
2003 EPSRC GR/S01276/01 Computational Challenges in Partial Differential Equations. (Principal Investigator).
2002 EPSRC GR/R40173/01 Computational Methods for Wave Propagation in Direct Scattering: An LMS
Durham Research Symposium. (Co-investigator).
2000 EPSRC Visiting Fellowship GR/N21970 - Dr W. McLean Multilevel preconditioners for boundary element methods on adaptively refined meshes. (Principal Investigator)
1999 EPSRC Visiting Fellowship GR/M55961 - Dr W. Dörfler Numerical analysis of convection diffusion
problems. (Principal Investigator).
1999 EPSRC GR/M59426 Computational Simulation of Electromagnetic Scattering. (Principal Investigator).
£78,000 plus additional funds to Prof. K. Morgan (Swansea University).
1998 EPSRC Visiting Fellowship GR/M09155 - Professor Benqi Guo Domain decomposition methods for
boundary element methods in three dimensions. (Principal Investigator).
1997 Australian Research Council A Post-processing and a posteriori error bounds for finite element analysis. (Associate Investigator. PIs were Prof. Kelly and Sloan, UNSW).
1997 EPSRC GR/L90507 Adaptive Methods for Singularly Perturbed Elliptic Systems. (Principal Investigator).
Numerical Analysis Summer Schools. ( 1994 Supported by EPSRC grant; 1996 Supported by
EPSRC grant and 1998 Supported by EPSRC under grant GR/M05034 ).
Numerous travel grants etc. from Royal Society, Glasgow Mathematical Journal, Edinburgh Mathematical
Society, London Mathematica Society, etc.
Member of Edinburgh Mathematical Society travel and research awards committee. 2003-2012.
Member of London Mathematical Society research meetings committee. 2003-2009.
Member of London Mathematical Society computer science committee. 2009-2012.
Member of Royal Society of Edinburgh sectional committee in mathematics. 2003-2005.
External examiner for MSc in Computational Mathematics at University of Manchester. 2004-2008.
External examiner for undergraduate final honours degree at Heriot-Watt University, Edinburgh. 2001-
2003.
External PhD Thesis Examiner
University of New South Wales, Norwegian Institute of Science and Technology, University of Bath, University of Cape Town, ...
Member of EPSRC Mathematics Peer Review College 1997–present.
Member of SIAM; London Mathematical Society; Edinburgh Mathematical Society.
Journal Reviews: Regularly review papers for many leading international journals in mathematics, scientific computing and engineering.
Book Reviews: Published book reviews in SIAM Review, Mathematics of Computation and Mathematical Reviews.
Year | Degree | Institution |
---|---|---|
1989 | PhD | Durham University |
1986 | BS | Durham University |
Member of London Mathematical Society research meetings committee. 2003-2009.
Member of London Mathematical Society computer science committee. 2009-2012.
Member of Royal Society of Edinburgh sectional committee in mathematics. 2003-2005.
External examiner for MSc in Computational Mathematics at University of Manchester. 2004-2008.
External examiner for undergraduate final honours degree at Heriot-Watt University, Edinburgh. 2001-
2003.
External PhD Thesis Examiner
University of New South Wales, Norwegian Institute of Science and Technology, University of Bath, University of
Cape Town
Member of EPSRC Mathematics Peer Review College 1997–present.
Member of SIAM; London Mathematical Society; Edinburgh Mathematical Society.
Member of editorial board of SIAM Journal on Numerical Analysis (2013-present).
Member of editial board of IMA Journal on Numerical Analysis (2004-present).
Member of editorial board of SIAM Journal on Scientific Computing 2001-2016 (Served five terms).
Senior Editor of Applied Numerical Mathematics (2003-2013). Associate editor (1998-2003).
Member of editorial board of Journal on Scientific Computing 2012-2014.
Member of editorial board of International Journal for Numerical Methods in Engineering (2003-present).
Member of editorial board of International Journal of Numerical Analysis and Modelling (2004-2012).
Member of editorial board of Numerical Methods for Partial Differential Equations (2004-present).
Member of editorial board of International Journal for Numerical Methods in Fluids (2005-present).
Member of editorial board of Proceedings of Royal Society of Edinburgh. (2003-2007). Section A: Mathematics (2003-2007). Invited to become Editor-in-Chief 2008 (declined).
London Mathematical Society Prize Committee 2014–2016
Director of Centre for Numerical Algorithms and Intelligent Software, 2011-2012. £5M multi-disciplinary centre formed by Universities of Strathclyde, Edinburgh, Heriot-Watt and Edinburgh Parallel Computing Centre. Ainsworth was one of four founding members of the centre.
Mathematical Sciences Research Institute (Berkeley): Programme on Numerical and Applied Mathematics
(6th March-28th April 2000). Co-organiser along with Professors Babuška, Bank and Verfürth, of MSRI workshop on A Posteriori Error Estimation and Adaptive Approaches in the Finite Element Method supported by MSRI and NSF.
Isaac Newton Institute for Mathematical Sciences (Cambridge): Programme on Computational Challenges
in Partial Differential Equations held in Cambridge, January-July 2003. Co-organiser with Professors
C.M. Elliot and E. Süli.
EMS Prize Committee: Member of prize committee of Edinburgh Mathematical Society 2004-2012.
Leslie Fox Prize Committee: Member of prize committee for Leslie Fox Prize in Numerical Analysis
2008-2013. Chair of adjudicating panel 2013.
APMA 2560 - Numerical Solution of Partial Differential Equations II |
APMA 2570B - Numerical Solution of Partial Differential Equations III |
APMA 2811R - Domain Decomposition and Multigrid for Finite Element Methods |