Discretization methods for approximating the Partial Differential Equations (PDEs):

- Finite Difference (FD)
- Finite Elements (FE)
- Finite Volume (FV)

#### Finite Difference (FD)

Taylor’s polynomial

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# Category: Tutorial

## Computational Fluid Dynamics (CFD)

#### Finite Difference (FD)

## Modular Arithmetic Library

###### -GitHub repository:

###### -Article

## Fluid Dynamics

#### Conservation of mass

## RNN, LSTM & GRU

## Convolutional Neural Network (CNN)

### Introduction

### Notation

## Elliptic Curve Algorithm (ECC)

### General definition

C++, UE4, AI developer

Navier-Stokes + Incompressible + Finite difference method

Discretization methods for approximating the Partial Differential Equations (PDEs):

- Finite Difference (FD)
- Finite Elements (FE)
- Finite Volume (FV)

Taylor’s polynomial

Modular Arithmetic Library in C++

This library provides the basics of modular arithmetic operations:

- Great Common Divisor (GCD)
- Least Common Multiple (LCM)
- Bezout solver
- Decomposition number algorithm
- Euler’s totient function
- Primality Test
- Find next Prime
- Inverse function
- Solver for 1 equation
- Solver for multiple equations

Modular Arithmetic Source Code

Navier-Stokes Equation

[] : fluid density

[] : dynamic viscosity

[] : kinematic viscosity

[] : velocity

: volume

- For a system:
- For a C.V. (Reynolds transport theorem):\]

Differential form (\delta x\delta y\delta z):

Recurrent Neural Network (RNN), Long-Short Term Memory (LSTM) & Gated Recurrent Unit (GRU)

Is a type of artificial neural network where connections between nodes form a sequence. This allows temporal dynamic behavior for time sequence.

There are 3 types of vanilla recurrent neural network: the simple (RNN), gated recurrent unit (GRU) and long short term memory unit (LSTM).

Convolutional neural network introduction and tutorial

Convolutional neural network (CNN or ConvNet) is a type of neural network used in artificial intelligence that is commonly applied to analyzing images.

They can be considered a pre-processing compared to image classification algorithms. They have applications in image and video recognition, recommender systems, image classification, natural language processing, etc.

: filter size.

: padding.

: stride.

: input.

: output.

.

: filter.

: activation function.

: bias.

ECC operations and performance

Elliptic curves (ECC) are a plane algebraic curve with the form:

where and are elements such that does not have double root.