### 2018

Reinarz, Anne and Dodwell, Tim and Fletcher, Timothy and Seelinger, Linus and Butler, Richard and Scheichl, R. Dune-composites ? A new framework for high-performance finite element modelling of laminates. Composite Structures. 184, 269–278 (2018) Total: 1

### 2017

Shardlow, T. and Kloeden, Peter. Gauss-quadrature method for one-dimensional mean-field SDEs. SIAM Journal on Scientific Computing. (2017) Kyprianou, Andreas and Osojnik, Ana and Shardlow, T. Unbiased walk-on-spheres Monte Carlo methods for the fractional Laplacian. IMA Journal of Numerical Analysis. (2017) Budd, C. and Glendinning, Paul and Hill, Kaitlin and Kuske, Rachel. Characterizing tipping in a stochastic reduced stommel-type model in higher-dimensions. Extended Abstracts Spring 2016. Birkhauser 25–29 (2017)Mora, Karin and Budd, C. Non-smooth hopf-type and grazing bifurcations arising from impact/friction contact events. Extended Abstracts Spring 2016. Birkhauser 129–134 (2017)Shardlow, T. and Marsland, Stephen. Langevin equations for landmark image registration with uncertainty. SIAM Journal on Imaging Sciences. 10 (2), 782–807 (2017) Gazzola, S. and Wiaux, Yves. Fast nonnegative least squares through flexible Krylov subspaces. SIAM Journal on Scientific Computing. 39 (2), A655—A679 (2017) Duarte, Roberto and Chen, Zhouye and Gazzola, S. and Marshall, Ian and Davies, Mike and Wiaux, Yves. Convex optimisation for partial volume estimation in compressive quantitative MRI. . (2017)Room, Graham and Spence, A. and Evangelou, Evangelos and Zeppini, Paolo and Pugliese, Emanuele and Napolitano, Lorenzo. Dynamics of cumulative innovation in complex social systems (DCICSS). University of Bath (2017)Dolgov, S. and Stoll, Martin. Low-rank solution to an optimization problem constrained by the Navier-Stokes equations. SIAM Journal on Scientific Computing. 39 (1), A255–A280 (2017) Aouaichia, Mustapha and McCullen, Nicholas and Bowen, Christopher and Almond, Darryl and Budd, C. and Bouamrane, R. Understanding the anomalous frequency responses of composite materials using very large random resistor-capacitor networks. European Physical Journal B. 90 (3), (2017) Benner, Peter and Dolgov, S. and Khoromskaia, Venera and Khoromskij, Boris N. Fast iterative solution of the Bethe—Salpeter eigenvalue problem using low-rank and QTT tensor approximation. Journal of Computational Physics. 334, 221–239 (2017) Graham, I. and Spence, E. and Vainikko, Eero. Recent results on domain decomposition preconditioning for the high-frequency Helmholtz equation using absorption. Modern Solvers for Helmholtz Problems. Birkhäuser Basel (2017) Total: 12

### 2016

Budd, C. and Cullen, Mike and Piccolo, Chiara. Improving weather forecasting accuracy by using r-adaptive methods coupled to data assimilation algorithms. UK Success Stories in Industrial Mathematics. Springer International Publishing AG 11–18 (2016)Fletcher, Timothy and Reinarz, Anne and Dodwell, Timothy and Butler, Richard and Scheichl, R. and Newley, Richard. Efficient Modelling and Accurate Certification of Curved Aerospace Laminates. ECCM17 - 17th European Conference on Composite Materials. (2016)Peterseim, Daniel and Scheichl, R. Robust numerical upscaling of elliptic multiscale problems at high contrast. Computational Methods in Applied Mathematics. 16 (4), 579–603 (2016) Freitag, M. and Kürschner, Patrick and Pestana, Jennifer. GMRES convergence bounds for eigenvalue problems. Journal of Computational and Applied Mathematics. (2016) Mitchell, Lawrence and Müller, E. High level implementation of geometric multigrid solvers for finite element problems:applications in atmospheric modelling. Journal of Computational Physics. 327, (2016) Gazzola, S. and Reichel, Lothar. A new framework for multi-parameter regularization. BIT Numerical Mathematics. 56 (3), 919–949 (2016) Gazzola, S. and Onunwor, Enyinda and Reichel, Lothar and Rodriguez, Giuseppe. On the Lanczos and Golub-Kahan reduction methods applied to discrete ill-posed problems. Numerical Linear Algebra with Applications. 23 (1), 187–204 (2016) Gazzola, S. and Novati, Paolo. Inheritance of the discrete Picard condition in Krylov subspace methods. BIT Numerical Mathematics. 56 (3), 893–918 (2016) Gazzola, S. and Karapiperi, Anna. Image reconstruction and restoration using the simplified topological epsilon-algorithm. Applied Mathematics and Computation. 274, 539–555 (2016) Budd, C. and Chakhchoukh, Amine N. and Dodwell, Timothy J. and Kuske, Rachel. Chevron folding patterns and heteroclinic orbits. Physica D: Nonlinear Phenomena. 32–46 (2016) Butcher, J. C and Hill, A. T. and Norton, T. J. T. Symmetric general linear methods. BIT Numerical Mathematics. 56 (4), 1189–1212 (2016) Graham, I. and Scheichl, R. and Ullmann, Elisabeth. Mixed Finite Element Analysis of Lognormal Diffusion and Multilevel Monte Carlo Methods. Stochastics and Partial Differential Equations : Analysis and Computations. 4 (1), 41–75 (2016) Fletcher, Timothy A. and Kim, Tatiana and Dodwell, Timothy J. and Butler, Richard and Scheichl, R. and Newley, Richard. Resin treatment of free edges to aid certification of through thickness laminate strength. Composite Structures. 146, 26–33 (2016) Benner, Peter and Dolgov, S. and Onwunta, Akwum and Stoll, Martin. Low-rank solvers for unsteady Stokes-Brinkman optimal control problem with random data. Computer Methods in Applied Mechanics and Engineering. 304, 26–54 (2016) Budd, C. and Stockie, John M. Multilayer asymptotic solution for wetting fronts in porous media with exponential moisture diffusivity. Studies in Applied Mathematics. 136 (4), 424–458 (2016) Weller, Hilary and Browne, Philip and Budd, C. and Cullen, Mike. Mesh adaptation on the sphere using optimal transport and the numerical solution of a Monge-Ampére type equation. Journal of Computational Physics. 308, 102–123 (2016) Shardlow, T. and Taylor, Phillip. On the pathwise approximation of stochastic differential equations. BIT Numerical Mathematics. 56 (3), 1101–1129 (2016) Ferreiro-Castilla, Albert and Kyprianou, Andreas and Scheichl, R. An euler-poisson scheme for Lévy driven SDEs. Journal of Applied Probability. 53 (1), 262–278 (2016) Baskin, Dean and Spence, E. and Wunsch, Jared. Sharp high-frequency estimates for the Helmholtz equation and applications to boundary integral equations. SIAM Journal on Mathematical Analysis (SIMA). 48 (1), 229–267 (2016) Dedner, Andreas and Müller, E. and Scheichl, R. Efficient multigrid preconditioners for atmospheric flow simulations at high aspect ratio. International Journal for Numerical Methods in Fluids. 80 (1), 76–102 (2016) Total: 20

### 2015

Gazzola, S. and Novati, Paolo and Russo, Maria Rosaria. On Krylov projection methods and Tikhonov regularization. Electronic Transactions on Numerical Analysis. 44, 83–123 (2015) Budd, C. and Walsh, Emily and Russell, Robert. The geometry of r-adaptive meshes generated using optimal transport methods. Journal of Computational Physics. 282, 113–137 (2015) Aseeri, S. and Batrašev, O. and Icardi, M. and Leu, B. and Liu, A. and Li, N. and Muite, B. K. and Müller, Eike and Palen, B. and Quell, M. and Servat, H. and Sheth, P. and Speck, R. and Moer, M. Van and Vienne, J. Solving the Klein-Gordon equation using Fourier spectral methods:a benchmark test for computer performance. HPC '15 Proceedings of the Symposium on High Performance Computing. Society for Computer Simulation International 182–191 (2015)Dodwell, Timothy and Ketelsen, C. and Scheichl, R. and Teckentrup, A. L. A hierarchical multilevel Markov chain Monte Carlo algorithm with applications to uncertainty quantification in subsurface flow. SIAM/ASA Journal on Uncertainty Quantification. 3 (1), 1075–1108 (2015) Tang, Hui and Shardlow, T. and Owen, J. Michael. Use of fin equation to calculate nusselt numbers for rotating discs. Proceedings ASME Turbo Expo, 2015. American Society of Mechanical Engineers (ASME) V05CT00A001 (2015)Loisel, Sébastien and Nguyen, Hieu and Scheichl, R. Optimized Schwarz and 2-Lagrange multiplier methods for multiscale elliptic PDEs. SIAM Journal on Scientific Computing. 37 (6), A2896–A2923 (2015) Spence, E. Transform Methods for Linear PDEs. Encyclopedia of Applied and Computational Mathematics. Springer 1496–1500 (2015)Spence, E. Overview of Variational Formulations for Linear Elliptic PDEs. Unified Transform for Boundary Value Problems: Applications and Advances. SIAM 93–160 (2015)Müller, E. and Scheichl, R. and Vainikko, Eero. Petascale solvers for anisotropic PDEs in atmospheric modelling on GPU clusters. Parallel Computing. 50, 53–69 (2015) Tang, Hui and Shardlow, T. and Owen, J. Michael. Use of fin equation to calculate Nusselt numbers for rotating disks. Journal of Turbomachinery: Transactions of the ASME. 137 (12), 1 – 10 (2015) Budd, C. and Dold, J. W. and Galaktionov, V. A. Global blow-up for a semilinear heat equation on a subspace. Proceedings of the Royal Society of Edinburgh Section A - Mathematics. 145 (5), 893 – 923 (2015) Butler, Richard and Dodwell, Timothy J. and Kim, Tatiana and Kynaston, Stef and Scheichl, R. and Haftka, Raphael T. and Kim, Nam H. Uncertainty quantification of composite structures with defects using multilevel monte carlo simulations. Proceedings of the 17th AIAA Non-Deterministic Approaches Conference. American Institute of Aeronautics and Astronautics Inc. (2015)Kim, Tatiana and Fletcher, Timothy and Dodwell, Timothy and Butler, Richard and Scheichl, R. and Ankersen, Jesper and Newley, Richard. The effect of free edges on inter-laminar performance of curved laminates. proceedings of the 56th AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference. American Institute of Aeronautics and Astronautics Inc. (2015)Hill, A. T. and Norton, Terence. An iterative starting method to control parasitism for the Leapfrog method. Applied Numerical Mathematics. 87 (1), 145 (2015) Jenkins, Sian and Smith, Nathan and Budd, C. and Freitag, M. The effect of numerical model error on data assimilation. Journal of Computational and Applied Mathematics. 290, 567–588 (2015) Müller, E. and Scheichl, R. and Shardlow, T. Improving multilevel Monte Carlo for stochastic differential equations with application to the Langevin equation. Proceedings of the Royal Society A. 471 (2176), (2015) Graham, I. and Kuo, F. Y. and Nichols, J. A. and Scheichl, R. and Schwab, Ch and Sloan, I. H. Quasi-Monte Carlo finite element methods for elliptic PDEs with lognormal random coefficients. Numerische Mathematik. 131 (2), 329–368 (2015) Gander, M. J. and Graham, I. and Spence, E. Applying GMRES to the Helmholtz equation with shifted Laplacian preconditioning:what is the largest shift for which wavenumber-independent convergence is guaranteed?. Numerische Mathematik. 131 (3), 567–614 (2015) Freitag, M. and Kürschner, Patrick. Tuned preconditioners for inexact two-sided inverse and Rayleigh quotient iteration. Numerical Linear Algebra with Applications. 22 (1), 175–196 (2015) Spence, E. and Kamotski, Ilia V. and Smyshlyaev, Valery P. Coercivity of combined boundary integral equations in high-frequency scattering. Communications on Pure and Applied Mathematics. 68 (9), 1587–1639 (2015) Graham, I. and Löhndorf, M. and Melenk, J. M. and Spence, E. When is the error in the h-BEM for solving the Helmholtz equation bounded independently of k ?. BIT Numerical Mathematics. 55 (1), 171–214 (2015) Spence, E. Bounding acoustic layer potentials via oscillatory integral techniques. BIT Numerical Mathematics. 55 (1), 279–318 (2015) Dauge, M. and Norton, R. A. and Scheichl, R. Regularity for Maxwell eigenproblems in photonic crystal fibre modelling. BIT Numerical Mathematics. 55 (1), 59–80 (2015) Total: 23

### 2014

Browne, P. A. and Budd, C. and Piccolo, C. and Cullen, M. Fast three dimensional r-adaptive mesh redistribution. Journal of Computational Physics. 275, 174–196 (2014) Gazzola, S. and Nagy, James G. Generalized arnoldi-tikhonov method for sparse reconstruction. SIAM Journal on Scientific Computing. 36 (2), (2014) Gazzola, S. and Novati, Paolo. Automatic parameter setting for Arnoldi-Tikhonov methods. Journal of Computational and Applied Mathematics. 256, 180–195 (2014) Gazzola, S. and Novati, P. and Russo, M. R. Embedded techniques for choosing the parameter in tikhonov regularization. Numerical Linear Algebra with Applications. 21 (6), 796–812 (2014) Mora, Karin and Budd, C. and Glendinning, Paul and Keogh, Patrick. Non-smooth Hopf-type bifurcations arising from impact-friction contact events in rotating machinery. Proceedings of the Royal Society A: Mathematical Physical and Engineering Sciences. 470 (2171), 20140490 (2014) Zhang, Zhipeng and Li, Jiangtao and Li, Furong and Budd, C. and Hamidi, Vandad. Assessment of DG security contribution on transmission levels. PES General Meeting/ Conference & Exposition, 2014 IEEE. IEEE (2014)Butcher, John C. and Habib, Yousaf and Hill, A. T. and Norton, Terence J T. The control of parasitism in G-symplectic methods. SIAM Journal on Numerical Analysis (SINUM). 52 (5), 2440–2465 (2014) Spillane, Nicole and Dolean, Victorita and Hauret, Patrice and Nataf, Frédéric and Pechstein, Clemens and Scheichl, R. Achieving robustness through coarse space enrichment in the two level Schwarz framework. Domain Decomposition Methods in Science and Engineering XXI.Vol. 98. Springer 447–455 (2014)Spence, E. Wavenumber-Explicit Bounds in Time-Harmonic Acoustic Scattering. SIAM Journal on Mathematical Analysis (SIMA). 46 (4), 2987–3024 (2014) Lord, Gabriel J. and Powell, Catherine E. and Shardlow, T. Introduction to Computational Stochastic PDEs. Cambridge University Press (2014)Alzubaidi, H. and Shardlow, T. Improved simulation techniques for first exit time of neural diffusion models. Communications in Statistics - Simulation and Computation. 43 (10), 2508–2520 (2014) Moiola, A. and Spence, E. Is the helmholtz equation really sign-indefinite?. Siam Review. 56 (2), 274–312 (2014) Freitag, M. and Spence, A. and Dooren, Paul Van. Calculating the H∞-norm Using the Implicit Determinant Method. SIAM Journal On Matrix Analysis and Applications (SIMAX). 35 (2), 619–635 (2014) Betcke, T. and Phillips, J. and Spence, E. Spectral decompositions and nonnormality of boundary integral operators in acoustic scattering. IMA Journal of Numerical Analysis. 34 (2), 700–731 (2014) Amodio, P. and Budd, C. and Koch, O. and Settanni, G. and Weinmüller, E. Asymptotical computations for a model of flow in saturated porous media. Applied Mathematics and Computation. 237, 155–167 (2014) Davenport, James H. and Wilson, David and Graham, I. and Sankaran, Gregory and Spence, A. and Blake, Jack and Kynaston, Stef. Interdisciplinary teaching of computing to mathematics students:Programming and discrete mathematics. MSOR Connections. 1–8 (2014) Müller, E. and Scheichl, R. Massively parallel solvers for elliptic partial differential equations in numerical weather and climate prediction:scalability of elliptic solvers in NWP. Quarterly Journal of the Royal Meteorological Society. 140 (685), 2608–2624 (2014) Ferreiro-Castilla, A. and Kyprianou, A.E. and Scheichl, R. and Suryanarayana, G. Multilevel Monte Carlo simulation for Lévy processes based on the Wiener?Hopf factorisation. Stochastic Processes and their Applications. 124 (2), 985–1010 (2014) Akinola, Richard O and Freitag, M. and Spence, A. The computation of Jordan blocks in parameter-dependent matrices. IMA Journal of Numerical Analysis. 34 (3), 955–976 (2014) Spillane, N. and Dolean, V. and Hauret, P. and Nataf, F. and Pechstein, C. and Scheichl, R. Abstract robust coarse spaces for systems of PDEs via generalized eigenproblems in the overlaps. Numerische Mathematik. 126 (4), 741–770 (2014) Akinola, R. O. and Freitag, M. and Spence, A. The calculation of the distance to a nearby defective matrix. Numerical Linear Algebra with Applications. 21 (3), 403–414 (2014) Total: 21

### 2013

Gazzola, S. and Novati, Paolo. Multi-parameter Arnoldi-Tikhonov methods. Electronic Transactions on Numerical Analysis. 40, 452–475 (2013) Freitag, M. Large Scale Inverse Problems:Computational Methods and Applications in the Earth Sciences. Walter de Gruyter (2013)Müller, E. and Guo, Xu and Scheichl, R. and Shi, Sinan. Matrix-free GPU implementation of a preconditioned conjugate gradient solver for anisotropic elliptic PDEs. Computing and Visualization in Science. 16 (2), 41–58 (2013) Freitag, M. and Spence, A. A new approach for calculating the real stability radius. BIT Numerical Mathematics. 54 (2), 381–400 (2013) Domínguez, V. and Graham, I. and Kim, T. Filon–Clenshaw–Curtis rules for highly oscillatory integrals with algebraic singularities and stationary points. SIAM Journal on Numerical Analysis (SINUM). 51 (3), 1542–1566 (2013) Freitag, M. and Potthast, Roland W E. Synergy of inverse problems and data assimilation techniques. Large Scale Inverse Problems. Walter de Gruyter (2013)Scheichl, R. Robust coarsening in multiscale PDEs. Domain Decomposition Methods in Science and Engineering XX. Springer 51–62 (2013)Pechstein, C. and Sarkis, M. and Scheichl, R. New theoretical coefficient robustness results for FETI-DP. Domain Decomposition Methods in Science and Engineering XX. Springer 313–320 (2013)Dolean, V. and Nataf, F. and Spillane, N. and Scheichl, R. A two-level Schwarz preconditioner for heterogeneous problems. Domain Decomposition Methods in Science and Engineering XX. Springer 87–94 (2013)Alzubaidi, Hasan and Shardlow, T. Interaction of waves in a one dimensional stochastic PDE model of excitable media. Discrete and Continuous Dynamical Systems - Series B. 18 (7), 1735–1754 (2013) Pechstein, C. and Scheichl, R. Weighted Poincaré inequalities. IMA Journal of Numerical Analysis. 33 (2), 652–686 (2013) Teckentrup, A.L. and Scheichl, R. and Giles, M.B. and Ullmann, E. Further analysis of multilevel Monte Carlo methods for elliptic PDEs with random coefficients. Numerische Mathematik. 125 (3), 569–600 (2013) Norton, R.A. and Scheichl, R. Planewave expansion methods for photonic crystal fibres. Applied Numerical Mathematics. 63, 88–104 (2013) Budd, C. J and Cullen, M. J. P. and Walsh, E. J. Monge–Ampére based moving mesh methods for numerical weather prediction, with applications to the Eady problem. Journal of Computational Physics. 236, 247–270 (2013) Charrier, Julia and Scheichl, R. and Teckentrup, Aretha L. Finite element error analysis of elliptic PDEs with random coefficients and its application to multilevel Monte Carlo methods. SIAM Journal on Numerical Analysis (SINUM). 51 (1), 322–352 (2013) Almond, D. P. and Budd, C. and Freitag, M. and Hunt, G. W. and McCullen, N. J. and Smith, N. D. The origin of power-law emergent scaling in large binary networks. Physica A: Statistical Mechanics and its Applications. 392 (4), 1004–1027 (2013) Freitag, M. and Nichols, N. K. and Budd, C. Resolution of sharp fronts in the presence of model error in variational data assimilation. Quarterly Journal of the Royal Meteorological Society. 139 (672), 742–757 (2013) Total: 17