Umberto Emanuele Villa

Phone: 408-334-0327

Umberto Villa is a postdoctoral researcher at the Center for Applied Scientific Computing. His research interest focuses on the numerical simulation of physical problems of practical relevance in various fields of engeneering, including porous media flow, petroleum industry, electromagnetism, thermodynamics, fluid-dynamics, and solid mechanics. His areas of expertise include numerical methods for partial differential equations (PDE), high performance computing, finite element analysis, numerical linear algebra, multigrid, PDE constrained optimization and fluid-dynamics.

Umberto earned his Ph.D. in Computational Mathematics from the department of Mathematics and Computer Science of Emory University under the direction of Prof. Alessandro Veneziani.

In his dissertation, Umberto developed a family of time-adaptive solvers for the incompressible Navier-Stokes equations. These solvers are based on a pressure-corrected algebraic factorization of the Navier-Stokes system and feature an intrinsic hierarchical nature, such that an accurate approximation of the pressure Schur complement is obtained by computing intermediate low-order guesses. Such solvers are then suitable for an adaptive selection of the time-step since the difference between the pressure at two successive correction steps provides a natural a-posteriori estimator with no additional computational cost.
Algorithms and preconditioners analyzed in his thesis were implemented in the parallel C++ code PAlAdINS (Parallel Algebraic Adaptive Incompressible Navier-Stokes solvers), based on the LifeV finite element libraries and the Trilinos linear algebra library.

Umberto joined LLNL in February 2013 as a postdoctoral researcher in Dr. P. Vassilevski group. His current work focuses on upscaling and multigrid techinques for the efficient solution of the algebraic linear system arising from mixed finite element discretization of saddle point problems. Specifically, Umberto is working on constructing highly accurate coarse (upscaled) finite element discretization schemes based on algebraic multigrid techniques. A main focus of his work is the construction of adaptive discretization spaces/schemes that can be effectively reused, e.g. in Monte Carlo simulations of multiphyscis phenomena with uncertain input data. The practical application that is motivating Umberto's research is related to subsurface porous media flow and petroleum industry problems, such as estimating the subsurface geological properties and predicting future performance of oil reservoirs based upon previous injection and extraction rates.

For more information on Umberto, please visit his profile on LinkedIn:
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Areas: Numerical analysis, computational science, high performance computing
Keywords: numerical PDES, finite element analysis, preconditioning, multigrid, upscaling, parallel computing

Selected Publications

  1. P. Vassilevski, U. Villa, A Mixed Formulation for the Brinkman Problem, submitted to SINUM (preprint)
  2. P. Vassilevski, U. Villa, A Block-Diagonal Algebraic Multigrid Preconditioner for the Brinkman Problem, Siam J. Sci. Comput., 2013 (preprint)
  3. T. Passerini, A. Quaini, U. Villa, A. Veneziani, S. Canic, Validation of an open source framework for the simulation of blood flow in rigid and deformable vessels, Int. J. Numer. Meth. Biomed. Engng., published on line, 2013 (preprint)
  4. K. W. Desmond, U. Villa, M. Newey, W. Losert, Characterizing the rheology of fluidized granular matter, Phys. Rev. E, 88, 032202, 2013 (preprint)
  5. A. Veneziani, U. Villa, ALADINS: an ALgebraic splitting time ADaptive solver for the Incompressible Navier-Stokes equations, Journal Comput Phys., 2012 (preprint: part1, part2)
  6. U. Villa, Scalable Efficient Methods for Incompressible Fluid-dynamics in Engineering Problems, PhD Thesis, Emory University (link)

Conference Proceedings

  1. J. Slawinski, T. Passerini, U. Villa, A. Veneziani, V. Sunderman, Issues in Communication Heterogeneity for Message-Passing Concurrent Computing, Proceedings of the 22nd International Heterogeneity in Computing Workshop, 2013
  2. J. Slawinski, T. Passerini, U. Villa, A. Veneziani, V. Sunderman, Experiences with Target-Platform Heterogeneity in Clouds, Grids, and On-Premises Resources, Proceedings of the 21st International Heterogeneity in Computing Workshop, 2012 (preprint)


  • LifeV ( A parallel C++ Finite element library providing implementations of state of the art mathematical and numerical methods. 
  • MFEM ( a general, modular, parallel C++ library for finite element methods research and development.
  • t-minres ( A templated parallel C++ implementation of the MINRES algorithm

External Collaborators