High-Performance Numerical Implementation: From Mathematical Theory to Optimized Execution

Full Metal Analytics provides specialized consultancy in the development and optimization of high-fidelity numerical models for resource-constrained environments.


We bridge the gap between complex mathematical theory and production-ready software, delivering optimized kernels designed for seamless integration into specialized hardware and high-performance software stacks.

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Our Engagement Model

01

Algorithmic Assessment

Rigorous mathematical auditing and performance benchmarking of existing models.

02

High-Fidelity Prototyping

Developing optimized Wasm, WebGPU, or C++ implementations to validate speed and accuracy.

03

Production Integration

Transitioning validated IP into specialized silicon, FPGA flows, or enterprise software stacks.

Numerical Kernel Development

Creating stable, high-precision kernels designed for minimal memory footprint and maximum computational throughput.

Hardware-Aware Optimization

Bridging the gap between complex mathematical models and the constraints of low-level hardware execution.

Computational Profiling

Rigorous benchmarking of algorithmic efficiency to identify and resolve performance bottlenecks.

Targeted Computational Domains

Real-Time Simulation | Semiconductor EDA | High-Performance Computing | Quantitative Finance

Proven Implementation Modules

Our technical library includes optimized kernels designed to demonstrate mathematical stability and execution speed.

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Derivative Pricing Kernels

Optimized pricing algorithms for resource-constrained deployment.

Gradient Engine Modules

High-speed automatic differentiation for hardware acceleration.

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Core Expertise

Algorithmic Optimization

Available

Specialized in reducing computational complexity for real-time systems.

Cross-Platform Deployment

Wasm / C++

Deploying high-performance math across web and desktop environments.

Hardware-Aware Design

Specialty

Ensuring algorithms are ready for specialized silicon and EDA flows.

About Full Metal Analytics

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Bridging the gap between mathematical complexity and computational reality.

Full Metal Analytics is a specialized technical consultancy founded by PhDs in Applied Mathematics. We solve the most critical challenge in modern high-performance computing: ensuring that sophisticated mathematical models can be translated into efficient, stable, and scalable code without sacrificing numerical precision.


Mathematical Rigor & Stability

Numerical errors can invalidate even the most advanced models. Our expertise lies in the design and validation of robust numerical kernels. From adaptive mesh refinement (AMR) for complex PDEs to high-order finite element methods, we ensure that your algorithms maintain integrity under extreme computational loads and high-gradient dynamics.


High-Performance Implementation

We specialize in low-level performance engineering. By leveraging modern technologies such as WebGPU, WASM, and optimized C++ architectures, we transform theoretical algorithms into high-throughput implementations. Our goal is to maximize hardware utilization while minimizing the computational footprint.


Hardware-Software Co-Design

We approach every project with a hardware-aware lens. Whether preparing IP for specialized silicon, FPGA deployment, or EDA tool integration, we ensure that the software architecture is optimized for the specific memory hierarchies and parallel processing capabilities of your target environment.


Discuss a technical collaboration →

Project Consultation

Direct contact for consulting, licensing, or research collaboration.

By submitting, you consent to our processing of your data. Privacy Policy.

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Technical Capabilities

We provide high-fidelity numerical implementation services, bridging the gap between complex mathematical theory and optimized, hardware-ready execution.

Core Expertise

Sensitivities & Gradients

Automatic Differentiation (AAD)

Implementation of high-order sensitivity analysis, including edge-pushing techniques for automatic Hessian computation and efficient gradient tracking.

Dynamics & Evolution

PDE & Mesh Dynamics

Advanced solving for non-linear dynamics using adaptive mesh refinement (AMR) and high-fidelity solvers for complex boundary conditions.

Linear Systems

Numerical Linear Algebra

Development of optimized preconditioners and scalable solvers tailored for high-dimensional problems and large-scale systems.

Implementation

Hardware Optimization

Low-level performance engineering for SIMD architectures, GPU (WebGPU/CUDA), and FPGA-ready computational kernels.

Implementation Showcases

Click a module to launch a real-time technical demonstration.

Adaptive Mesh Dynamics

Launch Demo →

Reaction-Diffusion

Launch Demo →

Responsive Mesh Dynamics

Mesh adaptation is a vital mathematical tool for solving complex, high-gradient problems by concentrating computational resources where they are needed most. This demo was developed by our team of numerical analysts to showcase our expertise in advanced PDE solving.

Presets

Mathematical Settings

Visual Styles

Grid Colour
Color Mode
Chemtrail
Chessboard
Advanced settings
Boundary Conditions
Jacobi x0

Reaction-Diffusion: Adaptive Dynamics

Unlike traditional h or p-refinement, this demo utilizes an evolving moving mesh to concentrate resolution on high-gradient features. By optimizing the ratio of accuracy to degrees of freedom, we can achieve high-fidelity results with significantly fewer mesh points, carefully balancing mesh-update overhead against computational savings.

The Gray-Scott reaction-diffusion pattern generating model

Initial Conditions

Reaction Parameters

Mesh Settings

Moving mesh apation
Show grid

High-Speed 1D ADE Solver

. Simulation failed.




This solver implements an Alternating-Direction-Explicit (ADE) scheme to achieve high-speed simulation of advection-diffusion-reaction dynamics. The lack of a global dependency (which occurs in implicit methods where every point depends on every other point through the matrix solve) allows for massive scaling across thousands of processors, enabling rapid, real-time parameter exploration.

Domain: t > 0, xleft ≤ x ≤ xright

∂u/∂t = A ∂²u/∂²x + B ∂u/∂x + Cu + D

Initial: u(t=0, x) = u0(x)

Left BC: α0u + β0u' + γ0u'' = ε0

Right BC: αNu + βNu' + γNu'' = εN

Automatic Adjoint Differentiation (AAD)

Automatic Adjoint Differentiation (AAD) provides a mathematically exact way to compute sensitivities (gradients) without the prohibitive cost of finite difference methods. By propagating derivatives backward through the computational graph, AAD enables high-dimensional optimization and parameter estimation with a computational cost that is nearly independent of the number of input variables, making it a critical technology for real-time risk management and hardware-accelerated machine learning.

Source Code
def f(x, z):
    a = x + z
    b = x * z
    return 0.5 * sin(a) * cosh(b)

print(f(1,2, 1,0))
Input Console
Input
Expressions
Adjoint mode
Output Console

Research & Technical Insights

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Data Privacy Specification

At Full Metal Analytics, we apply the same rigor to data privacy as we do to our numerical kernels: we aim for maximum efficiency with minimal unnecessary overhead. We do not use tracking cookies, third-party marketing pixels, or invasive telemetry. We collect only what is required to facilitate professional technical inquiries and to maintain the security of our infrastructure.

1. Data Controller

The entity responsible for the processing of data on this website is:
Full Metal Analytics
Contact Email: mailbox@fullmetalanalytics.com

2. Data Processing Schema

We process data under specific legal bases defined by the UK GDPR.

Data Category Purpose Legal Basis
Inquiry Data
Name, Email, Organization, Requirements
To respond to professional inquiries and facilitate technical collaboration. Contractual Necessity
Technical Logs
IP Address, User-Agent, Access Logs
To ensure site security and maintain operational integrity. Legitimate Interest

3. Storage and International Transfers

Our infrastructure is hosted via Amazon Web Services (AWS). Data is primarily stored on servers located within the United Kingdom.

4. Data Retention Policy

We adhere to a principle of data minimization. Inquiry Data: Retained for not more than 24 months following your last correspondence with us. Technical Logs: Retained for 30 days for security auditing purposes, then automatically purged.

5. Your Rights

Under the UK GDPR, you hold the following rights regarding your personal data:

  • Right of Access: Request a copy of your data.
  • Right to Rectification: Request correction of inaccurate data.
  • Right to Erasure: Request deletion of your data ("Right to be forgotten").
  • Right to Restrict Processing: Limit how we use your data.
  • Right to Data Portability: Request your data in a machine-readable format.
  • Right to Object: Object to processing based on legitimate interests.

To exercise any of these rights, please contact us at mailbox@fullmetalanalytics.com.

6. Supervisory Authority

If you believe our processing of your data infringes upon your rights, you have the right to lodge a complaint with the Information Commissioner's Office (ICO), the UK supervisory authority for data protection.

15 June 2026 Version 3