Publications
Publications
Book Chapters
P. F. Antonietti, A. Cangiani, J. Collis, Z. Dong, E. H. Georgoulis, S. Giani, and P. Houston, Review of Discontinuous Galerkin Finite Element Methods for Partial Differential Equations on Complicated Domains. – In Barth, T.J., Griebel, M., Keyes, D.E., Nieminen, R.M., Roose, D., Schlick, T., editors, Lecture Notes in Computational Science and Engineering. Lecture Notes in Computational Science and Engineering, Springer, 2016
S. Giani and P. Houston, High-Order hp-Adaptive Discontinuous Galerkin Finite Element Methods for Compressible Fluid Flows. – In N. Kroll, H. Bieler, H. Deconinck, V. Couallier, H. van der Ven and K. Sorensen, editors, ADIGMA – A European Initiative on the Development of Adaptive Higher-Order Variational Methods for Aerospace Applications, Springer, 2010
Papers
S. Giani and M. Seaid (2019), Multi-hp adaptive discontinuous Galerkin methods for simplified PN approximations of 3D radiative transfer in non-gray media – International Journal for Numerical Methods in Engineering, Accepted.
H. Hakula and S. Giani (2020), On Effective Material Parameters of Thin Perforated Shells under Static Loading Journal: Computer Methods in Applied Mechanics and Engineering – Computer Methods in Applied Mechanics and Engineering 367, 113094.
S. Gu̩rin-Marthe, S. Nielsen, R. Bird, S. Giani, G. Di Toro (2019), Earthquake Nucleation Size: Evidence of Loading Rate Dependence in Laboratory Faults. РJournal of Geophysical Research: Solid Earth 124(1), 689-708.
T. Adams, S. Giani, W. Coombs (2019), A high-order elliptic PDE based level set reinitialisation method using a discontinuous Galerkin discretisation. – Journal of Computational Physics 379, 373-391.
R. Bird, W. Coombs, S. Giani (2019), A posteriori discontinuous Galerkin error estimator for linear elasticity. – Applied Mathematics and Computation 344-345, 78-96.
T. Adams, N. McLeish, S. Giani, W. Coombs (2019), A parabolic PDE based level set reinitialisation method using a discontinuous Galerkin discretisation. – Computers and Mathematics with Applications 78(9), 2944-2960.
A. Cangiani, G. Manolis, S. Giani, S. Metcalfe (2019), hp-adaptive discontinuous Galerkin methods for non-stationary convection-diffusion problems. – Computers and Mathematics with Applications 78(9), 3090-3104.
S. OÂ’Sullivan , R.E. Bird , W.M. Coombs , S. Giani (2019), Rapid non-linear finite element analysis of continuous and discontinuous Galerkin methods in MATLAB. – Computers and Mathematics with Applications 78(9), 3007-3026.
R. Bird, W. Coombs, S. Giani (2019), Accurate Configuration Force Evaluation via hp-adaptive Discontinuous Galerkin Finite Element Analysis. – Journal: Engineering Fracture Mechanics 216, 106370.
S. Giani (2019), An adaptive composite discontinuous Galerkin method for elliptic problems on complicated domains with discontinuous coefficients – Advances in Computational Mathematics 46(13), .
S. Giani (2018), hp-Adaptive Celatus Enriched Discontinuous Galerkin Method for Second-Order Elliptic Source Problems. – SIAM Journal on Scientific Computing 40(5), B1391-B1418.
S. Giani (2018), Reliable anisotropic-adaptive discontinuous Galerkin method for simplified P_N approximations of radiative transfer. – Computational and applied mathematics 337, 225-243.
S. Giani, L. Grubisic, H. Hakula and J. Ovall (2018), An a posteriori estimator of eigenvalue/eigenvector error for penalty-type discontinuous Galerkin methods. – Applied Mathematics and Computation 319(15), 562-574.
R. Bird, W. Coombs, S. Giani (2017), A quasi-static discontinuous Galerkin configurational force fracture propagation for brittle materials. – International Journal for Numerical Methods in Engineering 113(7), 1061-1080.
R. Bird, W. Coombs, S. Giani (2017), Fast native-MATLAB stiffness assembly for SIPG linear elasticity. – Computers & Mathematics with Applications 74(12), 3209-3230.
S. Giani, L. Grubisic, C. Engstrom (2016), Efficient and reliable hp-FEM estimates for quadratic eigenvalue problems and photonic crystal applications. – Computers and Mathematics with Applications 72(4), 952-973.
S. Giani, L. Grubisic and J. Ovall (2016), Benchmark results for testing adaptive finite element eigenvalue procedures part 2. – Applied Numerical Mathematics 102, 1-16.
S. Giani and M. Seaid (2016), hp-adaptive discontinuous Galerkin methods for simplified PN approximations of frequency-dependent radiative transfer. – Computer Methods in Applied Mechanics and Engineering 301, 52-79.
S. Giani, L. Grubisic, A. Meidlar and J. Ovall (2015), Robust estimates for hp-adaptive approximations of non-self-adjoint eigenvalue problems. – Numerische Mathematik 133(3), 471-495.
S. Giani (2015), hp-Adaptive Composite Discontinuous Galerkin Methods for Elliptic Eigenvalue Problems on Complicated Domains. – Applied Mathematics and computation 267, 604-617.
S. Giani (2015), Solving elliptic eigenvalue problems on polygonal meshes using discontinuous Galerkin composite finite element methods. – Applied Mathematics and computation 267, 618-631.
S. Giani, P. Houston (2014), hp-Adaptive Composite Discontinuous Galerkin Methods for Elliptic Problems on Complicated Domains. – Numerical Methods for Partial Differential Equations 30(4), 1342-1367.
S. Giani (2014), A hp-adaptive discontinuous Galerkin method for plasmonic waveguides. – Journal of Computational and Applied Mathematics 270, 12-20.
S. Giani, P. Houston (2014), Goal-Oriented Adaptive Composite Discontinuous Galerkin Methods for Incompressible Flows. – Journal of Computational and Applied Mathematics 270, 32-42.
P. Antonietti, S. Giani and P. Houston (2014), Domain Decomposition Preconditioners for Discontinuous Galerkin Methods for Elliptic Problems on Complicated Domains. – Journal of Scientific Computing 60(1), 203-227.
S. Giani, D. Schötzau and L. Zhu (2014), An a-posteriori error estimate for hp-adaptive DG methods for convection-diffusion problems on anisotropically refined meshes. – Computers and Mathematics with Applications 67, 869-887.
S. Giani, P. Houston (2013), Domain Decomposition Preconditioners for Discontinuous Galerkin Discretizations of Compressible Fluid Flows. – Numerical Mathematics: Theory, Methods and Applications 7(2), 123-148.
S. Giani, L. Grubisic and J. Ovall (2013), Error control for hp-adaptive approximations of semi-definite eigenvalue problems. – Computing 95(1), 235-257. Note: The legends for the convergence plots (Figures 2a, 4a, 6a, 7a, 9a, 10a) are incorrect. The green curves correspond to pure h-refinment, and the blue curves to hp-refinement. In all cases, the dashed curves correspond to our a posteriori error estimates.
P. Antonietti, S. Giani and P. Houston (2013), hp-version composite discontinuous Galerkin methods for elliptic problems on complicated domains. – SISC 35(3), A1417-A1439.
S. Giani (2013), An a posteriori error estimator for hp-adaptive continuous Galerkin methods for photonic crystal applications. – Computing 95(5), 395-414.
S. Giani (2013), High-order/hp-adaptive discontinuous Galerkin finite element methods for acoustic problems. – Computing 95(1), 215-234.
P. Solin and S. Giani (2013), An iterative adaptive hp-FEM method for non-symmetric elliptic eigenvalue problems. – Computing 95(1), 183-213.
S. Giani and E. Hall (2013), An a-posteriori error estimate for hp-adaptive DG methods for elliptic eigenvalue problems on anisotropically refined meshes. – Computing 95(1), 319-341.
D.J. Chappell, G. Tanner and S. Giani (2012), Boundary element dynamical energy analysis: a versatile method for solving two or three dimensional wave problems in the high frequency limit. – Journal of Computational Physics 231(18), 6181-6191.
S. Giani and P. Houston (2012), Anisotropic hp-adaptive discontinuous Galerkin finite element methods for compressible fluid flows. – International Journal of Numerical Analysis and Modeling 9(4), 928-949.
S. Giani and I.G. Graham (2012), Adaptive finite element methods for computing band gaps in photonic crystals. – Numerische Mathematik 121(1), 31-64.
S. Giani, L. Grubisic and J. Ovall (2012), Benchmark results for testing adaptive finite element eigenvalue procedures. – Applied Numerical Mathematics 62(2), 121-140.
S. Giani (2012), Convergent adaptive finite element methods for photonic crystal applications. – Mathematical Models and Methods in Applied Sciences (M3AS) 22(10), 1250028.
S. Giani (2012), An a posteriori error estimator for hp-adaptive discontinuous Galerkin methods for computing band gaps in photonic crystals. – Journal of Computational and Applied Mathematics 236(18), 4810-4826.
S. Giani and E. Hall (2012), An A Posteriori Error Estimator for Hp-Adaptive Discontinuous Galerkin Methods for Elliptic Eigenvalue Problems. – Mathematical Models and Methods in Applied Sciences (M3AS) 22(10), 1250030.
P. Solin and S. Giani (2012), An Iterative Adaptive Finite Element Method for Elliptic Eigenvalue Problems. – Journal of Computational and Applied Mathematics 236(18), 4582-4599.
D. Chappell, S. Giani and G. Tanner (2011), Dynamical energy analysis for built-up acoustic systems at high frequencies. – J. Acoust. Soc. Am. (JASA) 130(3), 1420-1429.
L. Zhu, S. Giani, P. Houston and D. Schötzau (2011), Energy Norm A-Posteriori Error Estimation for hp-Adaptive Discontinuous Galerkin Methods for Elliptic Problems in Three Dimensions. – Mathematical Models and Methods in Applied Sciences (M3AS) 21(2), 267-306.
S. Giani and I.G. Graham (2009), A convergent adaptive method for elliptic eigenvalue problems. – SIAM J. Numer. Anal. 47(2), 1067-1091.
Preprints
J. Readshaw and S. Giani, Using Company Specific Headlines and Convolutional Neural Networks to Predict Stock Fluctuations – arXiv.org, (2020)
S. Giani, L. Grubisic, A. Miedlar, J. S. Ovall, Robust estimates for hp-adaptive approximations of non-self-adjoint eigenvalue problems. – Matheon, (2013)
S. Giani, L. Grubisic and J. Ovall, Error control for hp-adaptive approximations of semi-definite eigenvalue problems. – Nottingham eprint, (2012)
P. Antonietti, S. Giani and P. Houston, hp-version composite discontinuous Galerkin methods for elliptic problems on complicated domains. – Nottingham eprint, (2012)
D.J. Chappell, G. Tanner and S. Giani, Boundary element dynamical energy analysis: a versatile method for solving two or three dimensional wave problems in the high frequency limit. – arXiv.org, (2012)
P. Antonietti, S. Giani and P. Houston, hp-Version composite discontinuous Galerkin methods for elliptic problems on complicated domains. – Nottingham eprint, (2011)
S. Giani and P. Houston, Anisotropic hp-adaptive discontinuous Galerkin finite element methods for compressible fluid flows. – Nottingham eprint, (2011)
S. Giani, L. Grubisic and J. Ovall, Reliable a-posteriori error estimators for hp-adaptive finite element approximations of eigenvalue/eigenvector problems. – arXiv.org, (2011)
S. Giani, An a posteriori error estimator for hp-adaptive discontinuous Galerkin methods for computing band gaps in photonic crystals. – Nottingham eprint, (2011)
S. Giani and E. Hall, An a posteriori error estimator for hp-adaptive discontinuous Galerkin methods for elliptic eigenvalue problems. – Nottingham eprint, (2011)
S. Giani, L. Grubisic and J. Ovall, Benchmark results for testing adaptive finite element eigenvalue procedures. – Nottingham eprint, (2011)
S. Giani, Convergent adaptive finite element methods for photonic crystal applications. – Nottingham eprint, (2011)
S. Giani and P. Houston, High-Order hp-Adaptive Discontinuous Galerkin Finite Element Methods for Compressible Fluid Flows. – Nottingham eprint, (2010)
S. Giani and I.G. Graham, Adaptive finite element methods for computing band gaps in photonic crystals. – Bath Institute for Complex Systems Preprint number 06/10, (2010)
D.J. Chappell, S. Giani and G. Tanner, Dynamical energy analysis for built-up acoustic systems at high frequencies. – arXiv.org, (2010)
L. Zhu, S. Giani, P. Houston and D. Schötzau, Energy Norm A-Posteriori Error Estimation for hp-Adaptive Discontinuous Galerkin Methods for Elliptic Problems in Three Dimensions. – Nottingham eprint, (2009)
S. Giani and I.G. Graham, A convergent adaptive method for elliptic eigenvalue problems and numerical experiments. – Bath Institute for Complex Systems Preprint number 14/08, (2008)
S. Giani, Convergence of Adaptive Finite Element Methods for Elliptic Eigenvalue Problems with Applications to Photonic Crystals. – Ph.D. Thesis, University of Bath, (2008)
S. Giani and I.G. Graham, A convergent adaptive method for elliptic eigenvalue. – Isaac Newton Institute for Mathematical Sciences Preprints NI07054-HOP, (2007)
S. Giani and I.G. Graham, A convergent adaptive method for elliptic eigenvalue problems. – Bath Institute for Complex Systems Preprint number 6/07, (2007)
Conference Papers
Stefano Giani, High-Order/hp-Adaptive Discontinuous Galerkin Finite Element Methods for Acoustic Problems. – International Symposium on the Computational Modelling and Analysis of Vehicle Body Noise and Vibration, , 2012
Edward J.C. Hall and Stefano Giani, Discontinuous Galerkin Methods for Eigenvalue Problems on Anisotropic Meshes. – ENUMATH 2011, ENUMATH 2011 Proceedings Volume, 2011
Gregor Tanner ,David Chappell, Hanya Ben Hamdin, Stefano Giani, Cathleen Seidel and Frank Vogel, Acoustic energy distribution in multi-component structures – Dynamical Energy Analysis versus numerically exact results – ISMA2010 International Conference on Noise and Vibration Engineering, 20-22 September, Leuven/Belgium, 2010
Gregor Tanner and Stefano Giani, Wave transport in complex vibro-acoustic structures in the high-frequency limit. – IUTAM Symposium on Vibration Analysis of Structures with Uncertainties, Proceedings of the IUTAM Symposium on the Vibration Analysis of Structures with Uncertainties held in St. Petersburg, Russia, July 5-9, 2009
Stefano Giani and Ivan G. Graham, Convergence of adaptive finite element methods for el liptic eigenvalue problems with applications to photonic crystals. – Mathematisches Forschungsinstitut Oberwolfach, Report No. 37/2009, 2009