About

Eric Polizzi is a Professor in the Department of Electrical and Computer Engineering at the University of Massachusetts Amherst, affiliated with the Riccio College of Engineering. He conducts computational activities at the intersection of various disciplines, including applied mathematics, physics, and nanoengineering. His research areas encompass materials and nanotechnology, with a focus on applying computational methods to problems in these fields. He holds a PhD in Applied Mathematics from the National Institute of Applied Sciences (INSA) in Toulouse, France, obtained in 2001. His educational background also includes a Master's degree in Physics and French degrees (Licence-Maitrise-DEA) from the University of Toulouse. Dr. Polizzi is recognized for his contributions to computational science and engineering, and he has received distinctions such as the NSF CAREER award. He is actively involved in professional societies including the Society for Industrial and Applied Mathematics (SIAM) and the Association for Computing Machinery (ACM). His work integrates applied mathematics, physics, and engineering to advance research in materials science and nanotechnology.

Research topics

• Computer Science
• Parallel computing
• Algorithm
• Applied mathematics
• Mathematical analysis
• Mathematics

Selected publications

• Nonlinear eigenvalue algorithm for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>G</mml:mi><mml:mi>W</mml:mi></mml:mrow></mml:math> quasiparticle equations

  Physical review. B./Physical review. B · 2025-01-17 · 3 citations

  articleSenior author

  The use of the Green's function in quantum many-body theory often leads to nonlinear eigenvalue problems, as the Green's function needs to be defined in the energy domain. The $GW$ approximation method is one typical example. In this article, we introduce a method based on the FEAST eigenvalue algorithm for accurately solving the nonlinear eigenvalue ${G}_{0}{W}_{0}$ quasiparticle equation. Based on the FEAST contour integral method for nonlinear eigenvalue problems, the energy (eigenvalue) domain is extended to the complex plane. A hypercomplex number is introduced to the calculation of the $GW$ self-energy to carry the imaginary parts of both Green's functions and FEAST contour quadrature nodes. Calculation results for various molecules are presented and compared with the more conventional graphical solution approximation method and spectral functions method. It is confirmed that the highest occupied molecular orbital from the Kohn-Sham (and Hartree-Fock) equation is very close to that of $GW$, while the lowest unoccupied molecular orbital shows noticeable differences.

  PublisherDOI

• Low-Rank SPIKE Framework for Solving Large Sparse Linear Systems with Applications

  ArXiv.org · 2025-04-15

  preprintOpen access

  The SPIKE family of linear system solvers provides parallelism using a block tridiagonal partitioning. Typically SPIKE-based solvers are applied to banded systems, resulting in structured off-diagonal blocks with non-zeros elements restricted to relatively small submatrices comprising the band of the original matrix. In this work, a low-rank SVD based approximation of the off-diagonal blocks is investigated. This produces a representation which more effectively handles matrices with large, sparse bands. A set of flexible distributed solvers, the LR-SPIKE variants, are implemented. There are applicable to a wide range of applications -- from use as a "black-box" preconditioner which straightforwardly improves upon the classic Block Jacobi preconditioner, to use as a specialized "approximate direct solver." An investigation of the effectiveness of the new preconditioners for a selection of SuiteSparse matrices is performed, particularly focusing on matrices derived from 3D finite element simulations. In addition, the SPIKE approximate linear system solvers are also paired with the FEAST eigenvalue solver, where they are shown to be particularly effective due to the former's rapid convergence, and the latter's acceptance of loose linear system solver convergence, resulting in a combination which requires very few solver iterations.

  PublisherOA PDFDOI

• One-Dimensional Plasmons and Hybridized Coupled Polaritons in Carbon Nanotubes

  The Journal of Physical Chemistry C · 2025-01-22 · 1 citations

  articleSenior authorCorresponding

  This paper presents real-time time-dependent density functional theory (TDDFT) ab initio simulations of selected armchair carbon nanotubes (CNTs). By scaling the lengths of CNTs, we provide a comprehensive analysis of the Tomonaga–Luttinger (T–L) 1-D plasmon velocities, confirming consistency with theoretical predictions and experimental observations. Our findings include detailed visual representations of excitation densities at various resonances. Furthermore, we explore the coupling between T–L plasmons and single electron excitations, identifying distinct 1-D polariton behaviors, such as strong harmonic generation due to nonlinearities, as well as energy gaps that differ from conventional 2-D polaritons. The study highlights the unique properties of armchair single-walled carbon nanotubes as low-loss nanocavity resonators, demonstrating potential applications in strong light-matter coupling and other nanophotonic devices. The simulation framework employed here opens avenues for further research into 1-D plasmonic phenomena and electronic spectroscopy in complex nanostructures.

  PublisherDOI

• Low‐Rank SPIKE Framework for Solving Large Sparse Linear Systems With Applications

  Numerical Linear Algebra with Applications · 2025-11-24

  articleOpen accessCorresponding

  ABSTRACT The SPIKE family of linear system solvers provides parallelism using a block tridiagonal partitioning. Typically SPIKE‐based solvers are applied to banded systems, resulting in structured off‐diagonal blocks with nonzeros elements restricted to relatively small submatrices comprising the band of the original matrix. In this work, a low‐rank SVD based approximation of the off‐diagonal blocks is investigated. This produces a representation which more effectively handles matrices with large, sparse bands. A set of flexible distributed solvers, the LR‐SPIKE variants, are implemented. These are applicable to a wide range of applications—from use as a “black‐box” preconditioner which straightforwardly improves upon the classic Block Jacobi preconditioner, to use as a specialized “approximate direct solver.” An investigation of the effectiveness of the new preconditioners for a selection of SuiteSparse matrices is performed, particularly focusing on matrices derived from 3D finite element simulations. In addition, the SPIKE approximate linear system solvers are also paired with the FEAST eigenvalue solver, where they are shown to be particularly effective due to the former's rapid convergence, and the latter's acceptance of loose linear system solver convergence, resulting in a combination which requires very few solver iterations.

  PublisherOA PDFDOI

• FEAST nonlinear eigenvalue algorithm for $GW$ quasiparticle equations

  arXiv (Cornell University) · 2024-09-10

  preprintOpen accessSenior author

  The use of Green's function in quantum many-body theory often leads to nonlinear eigenvalue problems, as Green's function needs to be defined in energy domain. The $GW$ approximation method is one of the typical examples. In this article, we introduce a method based on the FEAST eigenvalue algorithm for accurately solving the nonlinear eigenvalue $G_0W_0$ quasiparticle equation, eliminating the need for the Kohn-Sham wavefunction approximation. Based on the contour integral method for nonlinear eigenvalue problem, the energy (eigenvalue) domain is extended to complex plane. Hypercomplex number is introduced to the contour deformation calculation of $GW$ self-energy to carry imaginary parts of both Green's functions and FEAST quadrature nodes. Calculation results for various molecules are presented and compared with a more conventional graphical solution approximation method. It is confirmed that the Highest Occupied Molecular Orbital (HOMO) from the Kohn-Sham equation is very close to that of $GW$, while the Least Unoccupied Molecular Orbital (LUMO) shows noticeable differences.

  PublisherOA PDFDOI

• One-dimensional Plasmons and Hybridized Coupled Polaritons in Carbon Nanotubes

  arXiv (Cornell University) · 2024-11-01

  preprintOpen accessSenior author

  This paper presents real-time time-dependent density functional theory (TDDFT) ab-initio simulations of selected armchair carbon nanotubes (CNTs). By scaling the lengths of CNTs, we provide a comprehensive analysis of the Tomonaga-Luttinger (T-L) 1-D plasmon velocities, confirming consistency with theoretical predictions and experimental observations. Our findings include detailed visual representations of excitation densities at various resonances. Furthermore, we explore the coupling between T-L plasmons and single electron excitations, identifying distinct 1-D polariton behaviors, such as strong harmonic generation due to nonlinearities, as well as energy gaps that differ from conventional 2-D polaritons. The study highlights the unique properties of armchair SWCNTs as low-loss nanocavity resonators, demonstrating potential applications in strong light-matter coupling and other nanophotonic devices. The simulation framework employed here opens avenues for further research into 1-D plasmonic phenomena and electronic spectroscopy in complex nanostructures.

  PublisherOA PDFDOI

• A method of calculating bandstructure in real-space with application to all-electron and full potential

  Computer Physics Communications · 2023-11-17 · 2 citations

  articleSenior author
  PublisherDOI

• A method of calculating bandstructure in real-space with application to all-electron and full potential

  arXiv (Cornell University) · 2023-07-22

  preprintOpen accessSenior author

  We introduce a practical and efficient approach for calculating the all-electron full potential bandstructure in real space, employing a finite element basis. As an alternative to the k-space method, the method involves the self-consistent solution of the Kohn-Sham equation within a larger finite system that encloses the unit-cell. It is based on the fact that the net potential of the unit-cell converges at a certain radius point. Bandstructure results are then obtained by performing non-self-consistent calculations in the Brillouin zone. Numerous numerical experiments demonstrate that the obtained valence and conduction bands are in excellent agreement with the pseudopotential k-space method. Moreover, we successfully observe the band bending of core electrons.

  PublisherOA PDFDOI

• Automatic Differentiation for Inverse Problems with Applications in Quantum Transport

  arXiv (Cornell University) · 2023-07-18

  preprintOpen accessSenior author

  A neural solver and differentiable simulation of the quantum transmitting boundary model is presented for the inverse quantum transport problem. The neural solver is used to engineer continuous transmission properties and the differentiable simulation is used to engineer current-voltage characteristics.

  PublisherOA PDFDOI

• Automatic Differentiation for Inverse Problems with Applications in Quantum Transport

  2023-09-25 · 1 citations

  articleSenior author

  A neural solver and differentiable simulation of the quantum transmitting boundary model is presented for the inverse quantum transport problem. The neural solver is used to engineer continuous transmission properties and the differentiable simulation is used to engineer current-voltage characteristics.

  PublisherDOI

Recent grants

• CAREER: New Computational Paradigms for Large-scale ab-initio Simulations of Emerging Electronic Materials and Devices

  NSF · $400k · 2009–2014

• Collaborative Research: Developing a Robust Parallel Hybrid System Solver

  NSF · $154k · 2006–2009

• SI2-SSE: A parallel computing framework for large-scale real-space and real-time TDDFT excited-states calculations

  NSF · $486k · 2018–2022

• AF: Medium: Collaborative research: Advanced algorithms and high-performance software for large scale eigenvalue problems

  NSF · $470k · 2015–2019

Frequent coauthors

• Guojing Cong

  Oak Ridge National Laboratory

  152 shared

• David A. Bader

  152 shared

• Srinivas Aluru

  148 shared

• Felix Wolf

  Technical University of Darmstadt

  77 shared

• Xiaoye Sherry Li

  77 shared

• James Reinders

  ZRT Laboratory

  76 shared

• Meiyue Shao

  Fudan University

  76 shared

• Lawrence Rauchwerger

  76 shared

Awards & honors

• NSF CAREER award
• Society for Industrial and Applied Mathematics (SIAM)
• Association for Computing Machinery (ACM)