# 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.

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*

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.

## Publications

| 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.