Nonlinear Numerics Inc.

High-performance numerical solvers for complex physical systems.

We help research and engineering teams turn complex physical models into reliable and scalable simulation workflows when standard commercial tools fall short.

Services

Nonlinear Numerics Inc. helps research and engineering teams improve simulation workflows when existing tools lack the robustness, efficiency, or physical fidelity required for specialized modelling challenges. We work with your team to understand the modelling problem, identify the key numerical challenges, evaluate existing workflows or codebases where available, and scope a focused technical engagement that may include:

  • Diagnosing stability, robustness, accuracy, and performance issues in existing simulation workflows.
  • Implementing new physical models, solver capabilities, and performance optimizations within in-house codebases.
  • Adapting open-source software libraries to specialized modelling workflows.
  • Scaling research prototypes into maintainable, high-performance simulation tools.
  • Developing custom solvers based on adaptive high-order and structure-preserving numerical methods.
  • Designing verification, validation, and benchmarking workflows for scientific simulation codes.

Expertise

Numerical methods

  • Efficient adaptive high-order methods in space and time
  • Discontinuous Galerkin and spectral-element discretizations
  • Structure-preserving formulations, including energy-stable and entropy-stable methods
  • Stiffness-aware time integration for multiscale problems

Physics-based simulation

  • Nonlinear continuum models for fluids, solids, and plasmas
  • Computational fluid dynamics and magnetohydrodynamics
  • Geophysical and astrophysical flows
  • Kinetic plasma simulations, including particle-in-cell methods
  • Multiphysics, multiphase, and coupled systems

Scientific software engineering

  • Parallel computing (MPI, OpenMP) and GPU acceleration
  • Benchmarking, profiling, and performance optimization
  • Scaling research prototypes into maintainable simulation tools
  • Development and integration across C++/CUDA, Python, Julia, and Fortran codebases

Have a simulation challenge?

Nonlinear Numerics Inc. is based in Ottawa, Canada, and is available for select consulting engagements with academic research groups, industry R&D teams, and government laboratories across North America and internationally. To discuss a possible engagement, please send a brief note about the modelling problem, any progress to date, technical challenges you've encountered, and the timeline you have in mind.

Email: tristan@nonlinearnumerics.com

Some helpful details to provide, if available:

  • Organization and project context
  • Target model, simulation workflow, or solver capability
  • Relevant physics, governing equations, geometry, and initial/boundary conditions
  • Existing software stack/codebase, numerical approach, and progress to date in implementing the model or workflow
  • Main technical challenge: robustness, accuracy, runtime, scalability, or missing capability
  • Confidentiality, intellectual property, or publication constraints
  • Desired outcome, timeline, and expected scope of work