HELMHOLTZ-LERAY DECOMPOSITION IN MATRIX FIELD USINGWAVELET

• Main Author: Petrus Wijaya, Laurence
• Format: Final Project
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/36144
• Institution: Institut Teknologi Bandung

Helmholtz decomposition was discovered by Hermann von Helmholtz (1821-1894) in 1858 and is often referred to as one of the most important theorems in vector calculus. Helmholtz decomposition is often used in physics. For example, in an electric field, often what is known is not the electric vector field, but rather the divergence and curl of the electric field from Maxwell’s equation. From the decomposition, to review the electric field, it is sufficient to review the Coulomb force or its magnetic field. But Helmholtz decomposition will be difficult in the matrix field because we do not have the curl concept in the matrix field. For this reason, another method is needed to decompose it. One is to use the Leray projection and its decomposition is called Helmholtz-Leray decomposition. The Helmholtz decomposition results alone are not single because they involve a constant factor in derivatives. If the wavelet concept is used, decomposition will be single but local (depending on the domain being reviewed). This final project will discuss the decomposition of Helmholtz-Leray by using a wavelet so that it can be reviewed locally and has a single value.