[35] Kreusser, L.M., Lockyer, H.E., Müller, E.H. and Singh, P., 2024. Learning efficient and provably convergent splitting methods. submitted  arXiv:2411.09444.

[34] Müller, E.H., 2024. A Higher-order Hybridisable Discontinuous Galerkin IMEX method for the incompressible Euler equations. submitted arXiv:2410.09790

[33] Kazashi, Y., Müller, E.H. and Scheichl, R., 2024. Multigrid Monte Carlo Revisited: Theory and Bayesian Inference. submitted arXiv:2407.12149

[32] Deveney, T., Mueller, E.H. and Shardlow, T., 2023. Deep Surrogate Accelerated Delayed-Acceptance Hamiltonian Monte Carlo for Bayesian Inference of Spatio-Temporal Heat Fluxes in Rotating Disc Systems. SIAM/ASA Journal on Uncertainty Quantification, 11(3), pp.970-995. arXiv:2204.02272

[31] Müller, E.H., 2023. Exact conservation laws for neural network integrators of dynamical systems. Journal of Computational Physics, 488, p.112234. arXiv:2209.11661

[30] Malcolm, A., Müller, E.H. and Scheichl, R., 2023. Improving Met Office Weather and Climate Forecasts with Bespoke Multigrid Solvers. to appear arXiv:2307.04528

[29] Betteridge, J.D., Cotter, C.J., Gibson, T.H., Griffith, M.J., Melvin, T. and Müller, E.H., 2023. Hybridised multigrid preconditioners for a compatible finite‐element dynamical core. Quarterly Journal of the Royal Meteorological Society, 149(755), pp.2454-2476. arXiv:2210.11797

[28] Saunders, W.R., Grant, J. and Müller, E.H., 2021. A new algorithm for electrostatic interactions in Monte Carlo simulations of charged particles. Journal of Computational Physics, 430, p.110099. Vancouver arXiv:2006.16622

[27] Betteridge, J., Gibson, T.H., Graham, I.G. and Müller, E.H., 2021. Multigrid preconditioners for the hybridised discontinuous Galerkin discretisation of the shallow water equations. Journal of Computational Physics, 426, p.109948. arXiv:2004.09389

[26] Jansen, K., Müller, E.H. and Scheichl, R., 2020. Multilevel Monte Carlo algorithm for quantum mechanics on a lattice. Physical Review D, 102(11), p.114512. arXiv:2008.03090

[25] Maynard, C., Melvin, T. and Müller, E.H., 2020. Multigrid preconditioners for the mixed finite element dynamical core of the LFRic atmospheric model. Quarterly Journal of the Royal Meteorological Society, 146(733), pp.3917-3936.Vancouver arXiv:2002.00756

[24] Saunders, W.R., Grant, J. and Müller, E.H., 2020. Parallel Performance of ARM ThunderX2 for Atomistic Simulation Algorithms. arXiv preprintarXiv:2007.10054. .

[23] Saunders, W.R., Grant, J., Müller, E.H. and Thompson, I., 2020. Fast electrostatic solvers for kinetic Monte Carlo simulations. Journal of Computational Physics, 410, p.109379. arXiv:1905.04065

[22] Deveney, T., Mueller, E. and Shardlow, T., 2019. A deep surrogate approach to efficient Bayesian inversion in PDE and integral equation models.  arXiv:1910.01547

[21] Bastian, P., Müller, E.H., Müthing, S. and Piatkowski, M., 2019. Matrix-free multigrid block-preconditioners for higher order discontinuous Galerkin discretisations. Journal of Computational Physics, 394, pp.417-439. arXiv:1805.11930

[20] Adams, S.V., Ford, R.W., Hambley, M., Hobson, J.M., Kavčič, I., Maynard, C.M., Melvin, T., Müller, E.H., Mullerworth, S., Porter, A.R. and Rezny, M., 2019. LFRic: Meeting the challenges of scalability and performance portability in Weather and Climate models. Journal of Parallel and Distributed Computing, 132, pp.383-396. arXiv:1809.07267

[19] Galkowski, J., Müller, E.H. and Spence, E.A., 2019. Wavenumber-explicit analysis for the Helmholtz h-BEM: error estimates and iteration counts for the Dirichlet problem. Numerische Mathematik, 142(2), pp.329-357. arXiv:1608.01035

[18] Saunders, W.R., Grant, J. and Müller, E.H., 2018. A domain specific language for performance portable molecular dynamics algorithms. Computer Physics Communications, 224, pp.119-135. arXiv:1704.03329

[17] Katsiolides, G., Müller, E.H., Scheichl, R., Shardlow, T., Giles, M.B. and Thomson, D.J., 2018. Multilevel Monte Carlo and improved timestepping methods in atmospheric dispersion modelling. Journal of Computational Physics, 354, pp.320-343. arXiv:1612.07717

[16] Mitchell, L. and Müller, E.H., 2016. High level implementation of geometric multigrid solvers for finite element problems: applications in atmospheric modelling. Journal of Computational Physics, 327, pp.1-18. arXiv:1605.00492

[15] Dedner, A., Müller, E. and Scheichl, R., 2016. Efficient multigrid preconditioners for atmospheric flow simulations at high aspect ratio. International Journal for Numerical Methods in Fluids, 80(1), pp.76-102. arXiv:1408.2981

[14] Müller, E.H., Scheichl, R. and Vainikko, E., 2015. Petascale solvers for anisotropic PDEs in atmospheric modelling on GPU clusters. Parallel Computing, 50, pp.53-69. arXiv:1402.3545

[13] Müller, E.H., Scheichl, R. and Shardlow, T., 2015. Improving multilevel Monte Carlo for stochastic differential equations with application to the Langevin equation. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 471(2176), p.20140679. arXiv:1409.2342

[12] Aseeri, S., Batrašev, O., Icardi, M., Leu, B., Liu, A., Li, N., Muite, B.K., Müller, E., Palen, B., Quell, M. and Servat, H., 2015. Solving the Klein-Gordon equation using Fourier spectral methods: A benchmark test for computer performance. arXiv:1501.04552

[11] Müller, E.H. and Scheichl, R., 2014. Massively parallel solvers for elliptic partial differential equations in numerical weather and climate prediction. Quarterly Journal of the Royal Meteorological Society, 140(685), pp.2608-2624. arXiv:1307.2036

[10] Müller, E., Guo, X., Scheichl, R. and Shi, S., 2013. Matrix-free GPU implementation of a preconditioned conjugate gradient solver for anisotropic elliptic PDEs. Computing and Visualization in Science, 16, pp.41-58. arXiv:1302.7193

[9] Müller, E.H., Ford, R., Hort, M.C., Huggett, L., Riley, G. and Thomson, D.J., 2013. Parallelisation of the Lagrangian atmospheric dispersion model NAME. Computer Physics Communications, 184(12), pp.2734-2745.

[8] Dowdall, R.J., Colquhoun, B., Daldrop, J.O., Davies, C.T.H., Kendall, I.D., Follana, E., Hammant, T.C., Horgan, R.R., Lepage, G.P., Monahan, C.J. and Müller, E.H., 2012. The Upsilon spectrum and the determination of the lattice spacing from lattice-QCD including charm quarks in the sea. Physical Review D—Particles, Fields, Gravitation, and Cosmology, 85(5), p.054509. arXiv:1110.6887

[7] Gregory, E.B., Davies, C.T., Kendall, I.D., Koponen, J., Wong, K., Follana, E., Gámiz, E., Lepage, G.P., Müller, E.H., Na, H. and Shigemitsu, J., 2011. Precise B, B s, and B c meson spectroscopy from full lattice QCD. Physical Review D—Particles, Fields, Gravitation, and Cosmology, 83(1), p.014506. arXiv:1010.3848

[6] Müller, E.H., Hart, A., Horgan, R.R. and (HPQCD Collaboration), 2011. Renormalization of heavy-light currents in moving nonrelativistic QCD. Physical Review D—Particles, Fields, Gravitation, and Cosmology, 83(3), p.034501. arXiv:1011.1215

[5] Hart, A., von Hippel, G.M., Horgan, R.R. and Müller, E.H., 2009. Automated generation of lattice QCD Feynman rules. Computer Physics Communications, 180(12), pp.2698-2716.Vancouver arXiv:0904.0375

[4] Horgan, R.R., Khomskii, L., Meinel, S., Wingate, M., Foley, K.M., Lepage, G.P., von Hippel, G.M., Hart, A., Müller, E.H., Davies, C.T.H. and Dougall, A., 2009. Moving nonrelativistic QCD for heavy-to-light form factors on the lattice. Physical Review D—Particles, Fields, Gravitation, and Cosmology, 80(7), p.074505. arXiv:0906.0945

[3] Kubis, B., Müller, E.H., Gasser, J. and Schmid, M., 2007. Aspects of radiative K+ e3 decays. The European Physical Journal C, 50, pp.557-571. arXiv:hep-ph/0611366

[2] Müller, E.H., Kubis, B. and Meißner, U.G., 2006. T-odd correlations in radiative K+ ℓ3 decays and chiral perturbation theory. The European Physical Journal C-Particles and Fields, 48, pp.427-440. arXiv:hep-ph/0607151

[1] Hart, A. and Müller, E., 2004. Locality of the square-root method for improved staggered quarks. Physical Review D—Particles, Fields, Gravitation, and Cosmology, 70(5), p.057502. arXiv:hep-lat/0406030