Next-Generation Design and Simulation with SplitFXM

The end-to-end platform for physics-aware AI to build smarter digital twins and faster industrial simulations.

Powerful Features

SplitFXM provides a comprehensive toolkit for building robust digital twins and high-fidelity simulation workflows.

Scientific Machine Learning

Bridge the gap between traditional physics and modern AI. Seamlessly integrate with Python to make smarter, physics-aware predictions.

Ultra-High Precision

Achieve extreme accuracy in simulations with high-order numerical methods (Discontinuous Galerkin, Finite Element and Volume).

State-of-the-art Optimization Solvers

Robust approaches for solutions of highly stiff, non-linear models (using Block/Split Newton methods).

Universal Performance

High-performance parallel execution across hardware, from standard CPUs to NVIDIA and AMD GPUs.

Extreme Event Tracking

Capture sudden changes like shockwaves using advanced numerical methods (WENO/TENO schemes).

Real-World Flexibility

Adapts to complex, irregular shapes and real-world boundaries that standard simulation tools struggle with.

Adaptive Mesh Refinement

Dynamically adjusts the computational grid to focus resources where they're needed most.

Solver Comparison

How SplitFXM differs from traditional boundary value problem solvers?

SciPy's `solve_bvp` and Julia's `DifferentialEquations.jl`

Requires transformation of higher-order differential equations into first-order systems:

# Must convert to dy/dx = f(x,y,p) form
# Original equation: y'' + p*y' + q*y = g(x)
# Converted system:
# y1' = y2
# y2'  = g(x) - q*y1 - p*y2

Explicit Jacobian matrices must be provided for large-scale simulation problems:

# Must define df/dy and df/dp manually
# This becomes increasingly tedious for large systems

SplitFXM Approach

Work directly with governing equations in their natural form:

# Define equations as they appear in physics/engineering
# No need to transform to first-order systems
# res = d2x(y) + p*dx(y) + q*y - g(x)

Sparse Jacobians at runtime - Enhanced performance for large-scale digital twins

Comparison

For the Blasius Problem (η_max = 10, N = 100)

Method	Time (s)
SplitFXM++	~0.065
SciPy solve_bvp (no Jacobian)	~0.073

By focusing on the natural form of equations, SplitFXM makes it more intuitive and accessible while providing computational efficiency.

The “Split” Methodology

Our unique approach divides complex systems into multiple variable segments for more efficient computation.

1. System Division

Break down complex physical systems into manageable subsystems.

2. Variable Fixing

Hold some variables fixed while solving for others in each subsystem.

3. Iterative Solution

Alternate between subsystem solutions, gradually converging to the complete system solution.

4. Recursive Processing

Apply the same approach recursively for highly complex systems.

The “Split” Ecosystem

Our comprehensive suite of solvers for advanced simulation and digital twin challenges

“Divide and conquer for complex numerical solutions”

SplitNewton++

Core Split-Newton Solver for efficient non-linear system resolution.

SplitContin++: Numerical Continuation solver

Enables arc-length and one-point control for any arbitrary variable, essential for tracking solution branches.

SplitDAE++: General Differential-Algebraic Equation (DAE) Solver

Supports classic and advanced numerical integration schemes like Backward Differentiation Formulas (BDF) and Euler methods.

SplitOPS++: Operator-Splitting framework for DAEs

Implements various splitting schemes including Lie, Strang, and higher-order Suzuki methods for increased accuracy and stability in coupled systems.

SplitFXM++

The dedicated Multi-dimensional Boundary Value Problem (BVP) Solver, acting as the core integration engine. Architecture-independent parallelization across CPU and GPU (NVIDIA/AMD).

Python Side

SplitNewton & SplitFXM

Python implementations of the Split-Newton Solver and 1D BVP Solver.

Application Layer

ShockFXM++: Advanced Shock-Tube Simulator for analyzing wave propagation and discontinuities. View on GitHub

FlameletFXM++: Flamelet Solver specialized for combustion modeling in mixture-fraction space, vital for non-premixed flame analysis. Contact us

HypeSuite: Hypersonic Flow Calculation Suite based on SplitFXM. A comprehensive application featuring:

Atmosphere models, flight regimes, and trajectory integration
Inviscid/Viscous shock relations and surface inclination methods
Real gas thermodynamics, aero heating, and TPS estimation
Hypersonic vehicle design and L/D estimation

Watch SplitFXM++ in Action

See how SplitFXM++ handles complex real-world simulations with extreme accuracy and speed.

Application Domains

SplitFXM excels at solving challenging multi-dimensional problems across multiple scientific disciplines.

🌬️ Aerospace & Flows

Model gas dynamics, shock waves, and high-speed flight with precision.

🔥 Energy & Combustion

Simulate cleaner energy production and dynamic heat release.

🔋 Next-Gen Batteries

Optimize electric potential and ion transport for better battery cells.

❄️ Phase Changes

Track how materials transform between solid, liquid, and gas.

🌡️ Thermal Management

Advanced modeling of heat transfer for cooling and insulation.

⚗️ Industrial Chemistry

Optimize complex chemical reactions in manufacturing and energy.

⚡ Advanced Physics

Simulate ionized gases and plasma for future propulsion and energy.

🧲 Electromagnetic Fluids

Integrated modeling of fluids interacting with magnetic fields.

Pricing

Simple and transparent licensing options

License Type	Price	Intended Use	Action
Non-Commercial	Free	Research, educational, and personal use*	Download
Commercial	On Request	Business purposes or revenue-generating use	Request
C++ Version (including pre-requisites)**	On Request	For all purposes	Request

*Free version supports 1D only with limited numerical schemes
**For an example application, see ShockFXM++

Non-commercial use is licensed under Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0)

Have questions? Contact us

Citing SplitFXM

If you use SplitFXM in your research, please cite it using the following format:

@software{pavan_b_govindaraju_2025_14827049,
  author       = {Pavan B Govindaraju},
  title        = {gpavanb1/SplitFXM: v0.5.0},
  month        = feb,
  year         = 2025,
  publisher    = {Zenodo},
  version      = {v0.5.0},
  doi          = {10.5281/zenodo.14827049},
  url          = {https://doi.org/10.5281/zenodo.14827049},
}

SplitFXM is an open-source project. Your acknowledgment helps support its continued development.

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