Staff profile
Overview
https://apps.dur.ac.uk/biography/image/397
Affiliation | Telephone |
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Associate Professor in the Department of Engineering | +44 (0) 191 33 42397 |
Biography
I am an Associate Professor in High-Performance Computing within the Department of Engineeringat Durham University, specialising in Finite Element Methods (FEMs) that I applied to a varietyof linear and non-linear problems in solid mechanics, fluid dynamics, photonics, acoustics andradiative heat transfer. My research interests include discontinuous Galerkin methods, error estimators, adaptivity, multi-level methods, preconditioners and fracture.
I am also an expert in Deep Neural Networks (DNNs) to tackle a variety of problems such as AI-based machine monitoring systems, natural language processing and artificial language processing.
Research interests
- Finite Element Methods (FEMs) and Artificial Intelligence (AI).
Publications
Chapter in book
- The Good, the Bad, and the Ugly
Dallabona, A., & Giani, S. (in press). The Good, the Bad, and the Ugly. In A. Sikarskie (Ed.), Storytelling in Luxury Fashion: Brands, Visual Cultures, and Technologies. Routledge - Review of Discontinuous Galerkin Finite Element Methods for Partial Differential Equations on Complicated Domains
Antonietti, P., Cangiani, A., Collis, J., Dong, Z., Georgoulis, E., Giani, S., & Houston, P. (2016). Review of Discontinuous Galerkin Finite Element Methods for Partial Differential Equations on Complicated Domains. In G. Barrenechea, F. Brezzi, A. Cangiani, & E. Georgoulis (Eds.), Building bridges : connections and challenges in modern approaches to numerical partial differential equations (279-308). Springer Verlag. https://doi.org/10.1007/978-3-319-41640-3_9 - Chapter Chapter 28
Giani, S., & Houston, P. (2010). Chapter Chapter 28. In ADIGMA - A European Initiative on the Development of Adaptive Higher-Order Variational Methods for Aerospace Applications. https://doi.org/10.1007/978-3-642-03707-8_28
Conference Paper
- Modelling Fracture Behaviour in Fibre-Hybrid 3D Woven Composites
Weatherburn, A., Reinarz, A., Giani, S., & Szyniszewski, S. (2024, April). Modelling Fracture Behaviour in Fibre-Hybrid 3D Woven Composites. Presented at 2024 UK Association for Computational Mechanics Conference, Durham, UK - Immersed traction boundary conditions in phase field fracture modelling
Sims, B., Bird, R. E., Coombs, W. M., & Giani, S. (2024, April). Immersed traction boundary conditions in phase field fracture modelling. Presented at 2024 UK Association for Computational Mechanics Conference, Durham, UK - Recursive autoencoder network for prediction of CAD model parameters from STEP files
Miles, V., Giani, S., Vogt, O., & Kafieh, R. Recursive autoencoder network for prediction of CAD model parameters from STEP files - An investigation into the methods for modelling pre-existing cracks in phase field problems
Sims, B., Bird, R., Giani, S., & Coombs, W. (2023, April). An investigation into the methods for modelling pre-existing cracks in phase field problems. Presented at UKACM 2023, Warwick, UK - Classification of Pulmonary Hypertension by Shape Analysis of the Human Right Ventricle: Robustness and Preliminary Association with Clinical Outcomes
Desmond, E. L., Xu, J., Wong, T. C., Simon, M. S., Giani, S., & Brigham, J. C. (2019, December). Classification of Pulmonary Hypertension by Shape Analysis of the Human Right Ventricle: Robustness and Preliminary Association with Clinical Outcomes. Presented at 6th International Conference on Computational and Mathematical Biomedical Engineering, Sendai City, Japan - Level set based topology optimisation using high-order reinitialisation methods and the discontinuous Galerkin method
Adams, T., Giani, S., & Coombs, W. (2017, April). Level set based topology optimisation using high-order reinitialisation methods and the discontinuous Galerkin method. Presented at 25th Conference on Computational Mechanics UKACM 2017., Birmingham, UK - A discontinuous Galerkin hp-adaptive finite element method for brittlecrack propagation
Bird, R., Coombs, W., & Giani, S. (2017, December). A discontinuous Galerkin hp-adaptive finite element method for brittlecrack propagation. Presented at 25th UKACM Conference on Computational Mechanics, Birmingham, UK - Topology optimisation using level set methods and the discontinuous Galerkin method
Adams, T., Giani, S., & Coombs, W. (2023, March). Topology optimisation using level set methods and the discontinuous Galerkin method. Presented at ACME - UK 2016 24th Conference of the Association for Computational Mechanics in Engineering., Cardiff, UK - Two dimensional configurational-force-driven crack propagation using the discontinuous Galerkin method with rp-adaptivity
Bird, R., Coombs, W., & Giani, S. (2023, March). Two dimensional configurational-force-driven crack propagation using the discontinuous Galerkin method with rp-adaptivity. Presented at ACME - UK 2016 24th Conference of the Association for Computational Mechanics in Engineering., Cardiff, UK
Conference Proceeding
- UKACM Proceedings 2024
(2024, April). UKACM Proceedings 2024. Presented at 2024 UK Association for Computational Mechanics Conference, Durham, UK
Journal Article
- The Stress-Continuous Material Point Method: a technique to alleviate cell-crossing instability while retaining linear shape functions
Pretti, G., Bird, R., Coombs, W., Augarde, C., & Giani, S. (in press). The Stress-Continuous Material Point Method: a technique to alleviate cell-crossing instability while retaining linear shape functions. Computer Methods in Applied Mechanics and Engineering, - On shells of revolution with random profiles
Giani, S., Hakula, H., & Khuat, D. (2025). On shells of revolution with random profiles. Computer Methods in Applied Mechanics and Engineering, 444, Article 118081. https://doi.org/10.1016/j.cma.2025.118081 - Enhancing lecture capture with deep learning
Sales, R. M., & Giani, S. (2024). Enhancing lecture capture with deep learning. Advances in Engineering Software, 196, Article 103732. https://doi.org/10.1016/j.advengsoft.2024.103732 - An hp-adaptive discontinuous Galerkin method for phase field fracture
Bird, R. E., Augarde, C. E., Coombs, W. M., Duddu, R., Giani, S., Huynh, P. T., & Sims, B. (2023). An hp-adaptive discontinuous Galerkin method for phase field fracture. Computer Methods in Applied Mechanics and Engineering, 416, Article 116336. https://doi.org/10.1016/j.cma.2023.116336 - Convolutional neural network framework for wind turbine electromechanical fault detection
Stone, E., Giani, S., Zappalá, D., & Crabtree, C. (2023). Convolutional neural network framework for wind turbine electromechanical fault detection. Wind Energy, 26(10), 1082 - 1097. https://doi.org/10.1002/we.2857 - khp-adaptive spectral projection based discontinuous Galerkin method for the numerical solution of wave equations with memory
Giani, S., Engström, C., & Grubišić, L. (2023). khp-adaptive spectral projection based discontinuous Galerkin method for the numerical solution of wave equations with memory. Journal of Computational and Applied Mathematics, 429, Article 115212. https://doi.org/10.1016/j.cam.2023.115212 - Approaching STEP file analysis as a language processing task: A robust and scale-invariant solution for machining feature recognition
Miles, V., Giani, S., & Vogt, O. (2023). Approaching STEP file analysis as a language processing task: A robust and scale-invariant solution for machining feature recognition. Journal of Computational and Applied Mathematics, 427, Article 115166. https://doi.org/10.1016/j.cam.2023.115166 - Numerical solution of distributed-order time-fractional diffusion-wave equations using Laplace transforms
Engström, C., Giani, S., & Grubišić, L. (2023). Numerical solution of distributed-order time-fractional diffusion-wave equations using Laplace transforms. Journal of Computational and Applied Mathematics, 425, Article 115035. https://doi.org/10.1016/j.cam.2022.115035 - Recursive Encoder Network for the Automatic Analysis of STEP Files
Miles, V., Giani, S., & Vogt, O. (2023). Recursive Encoder Network for the Automatic Analysis of STEP Files. Journal of Intelligent Manufacturing, 34(1), 181-196. https://doi.org/10.1007/s10845-022-01998-x - On Effects of Concentrated Loads on Perforated Sensitive Shells of Revolution
Giani, S., & Hakula, H. (2023). On Effects of Concentrated Loads on Perforated Sensitive Shells of Revolution. Journal of Computational and Applied Mathematics, 428, Article 115165. https://doi.org/10.1016/j.cam.2023.115165 - Camera-Based System for the Automatic Detection of Vehicle Axle Count and Speed Using Convolutional Neural Networks
Miles, V., Gurr, F., & Giani, S. (2022). Camera-Based System for the Automatic Detection of Vehicle Axle Count and Speed Using Convolutional Neural Networks. International Journal of Intelligent Transportation Systems Research, 20(3), 778-792. https://doi.org/10.1007/s13177-022-00325-1 - A spectral projection based method for the numerical solution of wave equations with memory
Engström, C., Giani, S., & Grubišić, L. (2022). A spectral projection based method for the numerical solution of wave equations with memory. Applied Mathematics Letters, 127, Article 107844. https://doi.org/10.1016/j.aml.2021.107844 - Adaptive Configurational Force-based crack propagation for brittle and fatigue analysis
Bird, R., Coombs, W., & Giani, S. (2022). Adaptive Configurational Force-based crack propagation for brittle and fatigue analysis. International Journal for Numerical Methods in Engineering, 123(7), 1673-1709. https://doi.org/10.1002/nme.6911 - Higher Order Composite DG approximations of Gross–Pitaevskii ground state: benchmark results and experiments
Engström, C., Giani, S., & Grubišić, L. (2022). Higher Order Composite DG approximations of Gross–Pitaevskii ground state: benchmark results and experiments. Journal of Computational and Applied Mathematics, 400, Article 113652. https://doi.org/10.1016/j.cam.2021.113652 - Free Vibration of Perforated Cylindrical Shells of Revolution: Asymptotics and Effective Material Parameters
Giani, S., & Hakula, H. (2022). Free Vibration of Perforated Cylindrical Shells of Revolution: Asymptotics and Effective Material Parameters. Computer Methods in Applied Mechanics and Engineering, 403(A), Article 115700. https://doi.org/10.1016/j.cma.2022.115700 - An open source hp-adaptive discontinuous Galerkin finite element solver for linear elasticity
Wiltshire, T., Bird, R. E., Coombs, W. M., & Giani, S. (2022). An open source hp-adaptive discontinuous Galerkin finite element solver for linear elasticity. Advances in Engineering Software, 171, https://doi.org/10.1016/j.advengsoft.2022.103147 - Using Company-Specific Headlines and Convolutional Neural Networks to Predict Stock Fluctuations
Readshaw, J., & Giani, S. (2021). Using Company-Specific Headlines and Convolutional Neural Networks to Predict Stock Fluctuations. Neural Computing and Applications, 33(24), 17353-17367. https://doi.org/10.1007/s00521-021-06324-9 - On Effects of Perforated Domains on Parameter-Dependent Free Vibration
Giani, S., & Hakula, H. (2021). On Effects of Perforated Domains on Parameter-Dependent Free Vibration. Journal of Computational and Applied Mathematics, 394, Article 113526. https://doi.org/10.1016/j.cam.2021.113526 - Solving Elliptic Eigenproblems with Adaptive Multimesh hp-FEM
Giani, S., & Solin, P. (2021). Solving Elliptic Eigenproblems with Adaptive Multimesh hp-FEM. Journal of Computational and Applied Mathematics, 394, Article 113528. https://doi.org/10.1016/j.cam.2021.113528 - A Posteriori Error Estimates for Elliptic Eigenvalue Problems Using Auxiliary Subspace Techniques
Giani, S., Grubišic, L., Hakula, H., & Ovall, J. S. (2021). A Posteriori Error Estimates for Elliptic Eigenvalue Problems Using Auxiliary Subspace Techniques. Journal of Scientific Computing, 88(3), Article 55. https://doi.org/10.1007/s10915-021-01572-2 - Quasi-optimal mesh sequence construction through Smoothed Adaptive Finite Element Methods
Mulita, O., Giani, S., & Heltai, L. (2021). Quasi-optimal mesh sequence construction through Smoothed Adaptive Finite Element Methods. SIAM Journal on Scientific Computing, 43(3), A2211-A2241. https://doi.org/10.1137/19m1262097 - Smoothed-adaptive perturbed inverse iteration for elliptic eigenvalue problems
Giani, S., Grubišić, L., Heltai, L., & Mulita, O. (2021). Smoothed-adaptive perturbed inverse iteration for elliptic eigenvalue problems. Computational Methods in Applied Mathematics, 21(2), 385-405. https://doi.org/10.1515/cmam-2020-0027 - On Effective Material Parameters of Thin Perforated Shells under Static Loading
Giani, S., & Hakula, H. (2020). On Effective Material Parameters of Thin Perforated Shells under Static Loading. Computer Methods in Applied Mechanics and Engineering, 367, Article 113094. https://doi.org/10.1016/j.cma.2020.113094 - Multi-hp adaptive discontinuous Galerkin methods for simplified PN approximations of 3D radiative transfer in non-gray media
Giani, S., & Seaid, M. (2020). Multi-hp adaptive discontinuous Galerkin methods for simplified PN approximations of 3D radiative transfer in non-gray media. Applied Numerical Mathematics, 150, 252-273. https://doi.org/10.1016/j.apnum.2019.09.018 - An adaptive composite discontinuous Galerkin method for elliptic problems on complicated domains with discontinuous coefficients
Giani, S. (2020). An adaptive composite discontinuous Galerkin method for elliptic problems on complicated domains with discontinuous coefficients. Advances in Computational Mathematics, 46(1), Article 13. https://doi.org/10.1007/s10444-020-09759-1 - A parabolic level set reinitialisation method using a discontinuous Galerkin discretisation
Adams, T., McLeish, N., Giani, S., & Coombs, W. (2019). A parabolic level set reinitialisation method using a discontinuous Galerkin discretisation. Computers and Mathematics with Applications, 78(9), 2944-2960. https://doi.org/10.1016/j.camwa.2019.01.032 - hp-adaptive discontinuous Galerkin methods for non-stationary convection-diffusion problems
Cangiani, A., Georgoulis, E., Giani, S., & Metcalfe, S. (2019). hp-adaptive discontinuous Galerkin methods for non-stationary convection-diffusion problems. Computers and Mathematics with Applications, 78(9), 3090-3104. https://doi.org/10.1016/j.camwa.2019.04.002 - Accurate Configuration Force Evaluation via hp-adaptive Discontinuous Galerkin Finite Element Analysis
Bird, R., Coombs, W., & Giani, S. (2019). Accurate Configuration Force Evaluation via hp-adaptive Discontinuous Galerkin Finite Element Analysis. Engineering Fracture Mechanics, 216, Article 106370. https://doi.org/10.1016/j.engfracmech.2019.02.029 - A posteriori discontinuous Galerkin error estimator for linear elasticity
Bird, R., Coombs, W., & Giani, S. (2019). A posteriori discontinuous Galerkin error estimator for linear elasticity. Applied Mathematics and Computation, 344-345, 78-96. https://doi.org/10.1016/j.amc.2018.08.039 - A high-order elliptic PDE based level set reinitialisation method using a discontinuous Galerkin discretisation
Adams, T., Giani, S., & Coombs, W. (2019). A high-order elliptic PDE based level set reinitialisation method using a discontinuous Galerkin discretisation. Journal of Computational Physics, 379, 373-391. https://doi.org/10.1016/j.jcp.2018.12.003 - Rapid non-linear finite element analysis of continuous and discontinuous Galerkin methods in MATLAB
O'Sullivan, S., Bird, R., Coombs, W., & Giani, S. (2019). Rapid non-linear finite element analysis of continuous and discontinuous Galerkin methods in MATLAB. Computers and Mathematics with Applications, 78(9), 3007-3026. https://doi.org/10.1016/j.camwa.2019.03.012 - hp-adaptive celatus enriched discontinuous Galerkin method for second-order elliptic source problems
Giani, S. (2018). hp-adaptive celatus enriched discontinuous Galerkin method for second-order elliptic source problems. SIAM Journal on Scientific Computing, 40(5), B1391-B1418. https://doi.org/10.1137/17m1149912 - Reliable anisotropic-adaptive discontinuous Galerkin method for simplified P_N approximations of radiative transfer
Giani, S. (2018). Reliable anisotropic-adaptive discontinuous Galerkin method for simplified P_N approximations of radiative transfer. Journal of Computational and Applied Mathematics, 337, 225-243. https://doi.org/10.1016/j.cam.2017.12.039 - A quasi-static discontinuous Galerkin configurational force crack propagation method for brittle materials
Bird, R., Coombs, W., & Giani, S. (2018). A quasi-static discontinuous Galerkin configurational force crack propagation method for brittle materials. International Journal for Numerical Methods in Engineering, 113(7), 1061-1080. https://doi.org/10.1002/nme.5699 - Earthquake Nucleation Size: Evidence of Loading Rate Dependence in Laboratory Faults
Guérin‐Marthe, S., Nielsen, S., Bird, R., Giani, S., & Di Toro, G. (2018). Earthquake Nucleation Size: Evidence of Loading Rate Dependence in Laboratory Faults. Journal of Geophysical Research. Solid Earth, 124(1), 689-708. https://doi.org/10.1029/2018jb016803 - Fast native-MATLAB stiffness assembly for SIPG linear elasticity
Bird, R., Coombs, W., & Giani, S. (2017). Fast native-MATLAB stiffness assembly for SIPG linear elasticity. Computers and Mathematics with Applications, 74(12), 3209-3230. https://doi.org/10.1016/j.camwa.2017.08.022 - An a posteriori estimator of eigenvalue/eigenvector error for penalty-type discontinuous Galerkin methods
Giani, S., Grubišić, L., Hakula, H., & Ovall, J. (2017). An a posteriori estimator of eigenvalue/eigenvector error for penalty-type discontinuous Galerkin methods. Applied Mathematics and Computation, 319, 562-574. https://doi.org/10.1016/j.amc.2017.07.007 - Efficient and reliable hp-FEM estimates for quadratic eigenvalue problems and photonic crystal applications
Engström, C., Giani, S., & Grubišić, L. (2016). Efficient and reliable hp-FEM estimates for quadratic eigenvalue problems and photonic crystal applications. Computers and Mathematics with Applications, 72(4), 952-973. https://doi.org/10.1016/j.camwa.2016.06.001 - Robust error estimates for approximations of non-self-adjoint eigenvalue problems
Giani, S., Grubišić, L., Międlar, A., & Ovall, J. (2016). Robust error estimates for approximations of non-self-adjoint eigenvalue problems. Numerische Mathematik, 133(3), 471-495. https://doi.org/10.1007/s00211-015-0752-3 - Benchmark results for testing adaptive finite element eigenvalue procedures part 2 (conforming eigenvector and eigenvalue estimates)
Giani, S., Grubišić, L., & Ovall, J. (2016). Benchmark results for testing adaptive finite element eigenvalue procedures part 2 (conforming eigenvector and eigenvalue estimates). Applied Numerical Mathematics, 102, 1-16. https://doi.org/10.1016/j.apnum.2015.12.001 - hp-adaptive discontinuous Galerkin methods for simplified PN approximations of frequency-dependent radiative transfer
Giani, S., & Seaid, M. (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. https://doi.org/10.1016/j.cma.2015.12.013 - Solving elliptic eigenvalue problems on polygonal meshes using discontinuous Galerkin composite finite element methods
Giani, S. (2015). Solving elliptic eigenvalue problems on polygonal meshes using discontinuous Galerkin composite finite element methods. Applied Mathematics and Computation, 267, 618-631. https://doi.org/10.1016/j.amc.2015.01.011 - hp-Adaptive composite discontinuous Galerkin methods for elliptic eigenvalue problems on complicated domains
Giani, S. (2015). hp-Adaptive composite discontinuous Galerkin methods for elliptic eigenvalue problems on complicated domains. Applied Mathematics and Computation, 267, 604-617. https://doi.org/10.1016/j.amc.2015.01.031 - Goal-oriented adaptive composite discontinuous Galerkin methods for incompressible flows
Giani, S., & Houston, P. (2014). Goal-oriented adaptive composite discontinuous Galerkin methods for incompressible flows. Journal of Computational and Applied Mathematics, 270, 32-42. https://doi.org/10.1016/j.cam.2014.03.007 - A hp-adaptive discontinuous Galerkin method for plasmonic waveguides
Giani, S. (2014). A hp-adaptive discontinuous Galerkin method for plasmonic waveguides. Journal of Computational and Applied Mathematics, 270, 12-20. https://doi.org/10.1016/j.cam.2014.03.009 - hp–Adaptive composite discontinuous Galerkin methods for elliptic problems on complicated domains
Giani, S., & Houston, P. (2014). hp–Adaptive composite discontinuous Galerkin methods for elliptic problems on complicated domains. Numerical Methods for Partial Differential Equations, 30(4), 1342-1367. https://doi.org/10.1002/num.21872 - Domain Decomposition Preconditioners for Discontinuous Galerkin Methods for Elliptic Problems on Complicated Domains
Antonietti, P., Giani, S., & Houston, P. (2014). Domain Decomposition Preconditioners for Discontinuous Galerkin Methods for Elliptic Problems on Complicated Domains. Journal of Scientific Computing, 60(1), 203-227. https://doi.org/10.1007/s10915-013-9792-y - An a-posteriori error estimate for hp-adaptive DG methods for convection–diffusion problems on anisotropically refined meshes
Giani, S., Schötzau, D., & Zhu, L. (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(4), 869-887. https://doi.org/10.1016/j.camwa.2012.10.015 - High-order/hp-adaptive discontinuous Galerkin finite element methods for acoustic problems
Giani, S. (2013). High-order/hp-adaptive discontinuous Galerkin finite element methods for acoustic problems. Computing, 95(1 Supplement), S215-S234. https://doi.org/10.1007/s00607-012-0253-5 - An a posteriori error estimator for hp-adaptive continuous Galerkin methods for photonic crystal applications
Giani, S. (2013). An a posteriori error estimator for hp-adaptive continuous Galerkin methods for photonic crystal applications. Computing, 95(5), 395-414. https://doi.org/10.1007/s00607-012-0244-6 - Error control for hp -adaptive approximations of semi-definite eigenvalue problems
Giani, S., Grubišić, L., & Ovall, J. (2013). Error control for hp -adaptive approximations of semi-definite eigenvalue problems. Computing, 95(1), 235-257. https://doi.org/10.1007/s00607-012-0260-6 - An iterative adaptive hp-FEM method for non-symmetric elliptic eigenvalue problems
Solin, P., & Giani, S. (2013). An iterative adaptive hp-FEM method for non-symmetric elliptic eigenvalue problems. Computing, 95(1 Supplement), S183-S213. https://doi.org/10.1007/s00607-012-0251-7 - An a-posteriori error estimate for hp-adaptive DG methods for elliptic eigenvalue problems on anisotropically refined meshes
Giani, S., & Hall, E. (2013). An a-posteriori error estimate for hp-adaptive DG methods for elliptic eigenvalue problems on anisotropically refined meshes. Computing, 95(1 Supplement), S319-S341. https://doi.org/10.1007/s00607-012-0261-5 - hp-Version Composite Discontinuous Galerkin Methods for Elliptic Problems on Complicated Domains
Antonietti, P., Giani, S., & Houston, P. (2013). hp-Version Composite Discontinuous Galerkin Methods for Elliptic Problems on Complicated Domains. SIAM Journal on Scientific Computing, 35(3), A1417-A1439. https://doi.org/10.1137/120877246 - An a posteriori error estimator for hp-adaptive discontinuous Galerkin methods for computing band gaps in photonic crystals
Giani, S. (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. https://doi.org/10.1016/j.cam.2012.02.007 - An Iterative Adaptive Finite Element Method for Elliptic Eigenvalue Problems.
Solin, P., & Giani, S. (2012). An Iterative Adaptive Finite Element Method for Elliptic Eigenvalue Problems. Journal of Computational and Applied Mathematics, 236(18), 4582-4599. https://doi.org/10.1016/j.cam.2012.05.002 - An A Posteriori Error Estimator for Hp-Adaptive Discontinuous Galerkin Methods for Elliptic Eigenvalue Problems
Giani, S., & Hall, E. (2012). An A Posteriori Error Estimator for Hp-Adaptive Discontinuous Galerkin Methods for Elliptic Eigenvalue Problems. Mathematical Models and Methods in Applied Sciences, 22(10), https://doi.org/10.1142/s0218202512500303 - Convergent adaptive finite element methods for photonic crystal applications
Giani, S. (2012). Convergent adaptive finite element methods for photonic crystal applications. Mathematical Models and Methods in Applied Sciences, 22(10), https://doi.org/10.1142/s0218202512500285 - Boundary element dynamical energy analysis: a versatile method for solving two or three dimensional wave problems in the high frequency limit
Chappell, D., Tanner, G., & Giani, S. (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. https://doi.org/10.1016/j.jcp.2012.05.028 - Adaptive finite element methods for computing band gaps in photonic crystals
Giani, S., & Graham, I. (2012). Adaptive finite element methods for computing band gaps in photonic crystals. Numerische Mathematik, 121(1), 31-64. https://doi.org/10.1007/s00211-011-0425-9 - Benchmark results for testing adaptive finite element eigenvalue procedures
Giani, S., Grubisic, L., & Ovall, J. (2012). Benchmark results for testing adaptive finite element eigenvalue procedures. Applied Numerical Mathematics, 62(2), 121-140. https://doi.org/10.1016/j.apnum.2011.10.007 - Anisotropic hp-adaptive discontinuous Galerkin finite element methods for compressible fluid flows
Giani, S., & Houston, P. (2012). Anisotropic hp-adaptive discontinuous Galerkin finite element methods for compressible fluid flows. International journal of numerical analysis and modeling, 9(4), 928-949 - Dynamical energy analysis for built-up acoustic systems at high frequencies
Chappell, D., Giani, S., & Tanner, G. (2011). Dynamical energy analysis for built-up acoustic systems at high frequencies. The Journal of the Acoustical Society of America, 130(3), 1420-1429. https://doi.org/10.1121/1.3621041 - Energy Norm A-Posteriori Error Estimation for hp-Adaptive Discontinuous Galerkin Methods for Elliptic Problems in Three Dimensions
Zhu, L., Giani, S., Houston, P., & Schötzau, D. (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, 21(02), 267-306. https://doi.org/10.1142/s0218202511005052 - A convergent adaptive method for elliptic eigenvalue problems
Giani, S., & Graham, I. (2009). A convergent adaptive method for elliptic eigenvalue problems. SIAM Journal on Numerical Analysis, 47(2), 1067-1091. https://doi.org/10.1137/070697264
Supervision students
Anna Weatherburn
Research Postgraduate - Computational Mechanics Node
Bradley Sims
Research Postgraduate - Computational Mechanics Node
Cesar Higuera Higuera
Luke Macpherson
Soheil Navvabi
Research Postgraduate - Computational Mechanics Node