While modeling is the art of creating
mathematical models of reality, *simulation* is the art of using these mathematical
models to approximate reality inside a computer. In the industry, such computational
approximations of reality have important benefits compared to the naive strategy of
“just trying it out”:

- Lower cost of experimentation
- Reduced time of development
- Numerical optimization
- Less tedious

- Less hazardous
- “First time right”
- Vast array of experiments can be performed virtually

At Noumenon Multiphysics, we have the ability to use various simulation platforms to perform simulations. Chief among these is COMSOL — a multi-physics simulation platform having the ability to simulate and couple a large variety of physics and new mathematical models. Noumenon Multiphysics is a COMSOL certified consultant. Read more…

Other standard simulators used include OpenFOAM (fluid mechanics), Elmer (multiphysics), TracePro (optics), Simulink (system level simulation), SystemC (discrete event simulation), NS2 (data networks), GAP (multi-phase fluid flow) and many smaller simulation codes for specific phenomena.

## Custom Simulators

Apart from using standard simulation platforms, Noumenon also has the expertise to develop low level simulation codes. These are usually built in MATLAB, Python or C++. Even with the availability of multiple readymade simulation platforms, the need for custom simulation codes arises due to many reasons:

- Gaps in abilities of standard simulators, usually relating to specific applications
- New physics models developed at Noumenon Multiphysics, requiring new simulators
- Faster solution methods, employing known symmetries or features of particular situations
- Speciality simulators — codes that will go inside specialized software targeted towards very specific jobs
- Automated optimizers or parameter estimators can be built on top of simulation codes
- Cost effectiveness

## Example Projects

Though most Noumenon projects involve simulation, following are some projects showcasing custom simulator development:

**BIREFRINGENCE.**
Created models of
uniaxial and biaxial birefringence. The biaxial birefringence
model requires a modal decomposition of a non-linear equation,
which was solved using a novel non-linear Rayleigh quotient
method devised by us. These models were used to find birefringence
parameters of actual samples. Read more…

**FORCE BALANCE SOLVER.** Solves specific problems
involving linear elastic, non-linear elastic and rigid parts and
fluid pressure. Load-deformation curves of each individual body are
calculated separately. The force balance solver finds the final
resting position in which the entire system will settle.

**LENTICULAR OPTICS.**
We built a linear feedback theory based lenticular geometric optics solver, which was much faster than a generalized ray tracer can be. Read more…

**PERFORMANCE OF SEALS.**
We built new theory and simulation methods to predict the behavior of sealing solutions before they are manufactured and tested. Read more…

**LIGHT TRANSPORT.**
An integro-PDE equation was proposed for a class of light transport problems involving light guides made of bulk scattering material. The equation features not three but five geometric dimensions, three in differential and two in integral form. The integral form can be imagined to be a “spherical integration” — i.e. a linear shift invariant system where “shift” is defined using the symmetry group of a sphere. Read more…

**SHEPHERD ALGORITHM.** We created a new
algorithm to approximate multi-body interactions, with one elastic
and multiple rigid bodies. As the rigid bodies move, the shepherd
algorithm quickly creates a feasible solution which is heuristically
close to the final solution. Mechanical simulations involving multi-body
contact have shown vast speedup using this technique.

**MONTE-CARLO RAY TRACER.**
In this project, we built a generalized Monte-Carlo integration based light transport solver. The ray tracer can solve any problem involving light transport, geometric optics, media with indexes, mirrors, absorbers, etc. Read more…

**FEM WIRE SIMULATOR.** A finite element
simulator of metallic wire parts. Was commissioned as a validating
simulator for a large simulation platform.

**SOLAR OPTICS.** This simulator framework can calculate the position of the sun for any day of the year, and time of day, at any latitude. Furthermore, the simulator can calculate various shadowing effects applicable to objects such as heliostats (sun tracking mirrors). Averages of shadowing effects over time can be used to optimize placement, size etc. of these objects to maximize utilization of insolation.

**CIRCUIT SIMULATION WITH EM COMPONENTS.**
A new methodology was developed to convert the PDEs governing linear electromagnetic components to ODEs, for fast and accurate simulation of EM components as electronic circuit components.

**ELECTROMAGNETIC FEM.** Built our own FEM EM
solver to cross-check Mie scattering calculations, and to be able
to perform scattering calculations for irregular shaped objects.