Numerical Modelling & Simulations

Are you looking for ways how to model a physical process or simulate your data? Do you want to solve a differential equation or a system of those? Are you trying to speed up your algorithm?

At EZNumeric we have 15+ years of experience of developing numerical models and simulations as well as finding an efficient solution.

Areas of expertise

  • Numerical methods to solve large systems of linear equations, including preconditioner techniques (e.g. Krylov methods, multigrid)
  • Optimization / problem minimization algorithms (least squares, inversion)
  • Elliptic, parabolic and hyperbolic differential equations (wave equation, Helmholtz, streamline reservoir simulation, geoelectric modelling)
  • Compression: lossy or lossless
  • Finite differences, finite elements (continuous and discontinuous), finite volumes, meshless methods (e.g. material point method)

Programming languages

  • C/C++ object oriented
  • Fortran
  • Python
  • Matlab/Octave

Section through the tetrahedral mesh for finite element computations of the wave propagation. Made in collaboration with W.A. Mulder, S. Minisini, A. Kononov

Coarse grid correction coefficients for multigrid method in 3D
Fourier transform of frequency domain wave simulation with Marmousi velocity model

The following pictures shows the wavefront of a moving sound wave in a room. The blue surfaces (cube) and back-wall absorb the sound wave.

The animation can be found here. See the gallery for more example of computer generated images.


| A comparison of continuous mass-lumped finite elements with finite differences for 3-D wave propagation
| Time-stepping stability of continuous and discontinuous finite-element methods for 3-D wave propagation
| Local time stepping with the discontinuous Galerkin method for wave propagation in 3D heterogeneous media
| Stability and performance of the SIPG and IIPG finite-element methods for wave propagation
| Solving the 3D Acoustic Wave Equation with Higher-order Mass-lumped Tetrahedral Finite Elements
| A multigrid method with matrix-dependent transfer operators for 3D diffusion problems with jump coefficients
3D Helmholtz Krylov Solver Preconditioned by a Shifted Laplace Multigrid Method on Multi-GPUs
Reduction of computing time for least-squares migration based on the Helmholtz equation by graphics processing units

If you want to get a copy of our publications, please send us an email or fill in the contact form.