# Notation

This page lists the notation we use across the Bempp website, and may be a useful reference.

## Domains, surfaces, etc.

 Symbol(s) Meaning $\Omega$ A domain $\Omega^\text{--}$ An interior domain $\Omega^\text{+}$ An exterior domain $\Gamma$ The boundary of a domain $\nu$ The outward point normal to the surface $\Gamma$

## Points, vectors, etc.

 Symbol(s) Meaning Bold lowercase: $\mathbf{x}$, $\mathbf{y}$, … A point in 3D space $x$, $y$ and $z$ The three components of a point $\mathbf{x}$

## Operators and matrices

 Symbol(s) Meaning Curly capitals: $\mathcal{K}$, $\mathcal{V}$, … Potential operators Sans-serif capitals: $\mathsf{K}$, $\mathsf{V}$, … Boundary operators Serif capitals with subscripts: $K_h$, $V_h$, … Matrices arising from discretisation of an operator Serif capitals: $M$, $A$, … Other matrices $\mathcal{C}^\text{--}$, $\mathcal{C}^\text{+}$ Interior and exterior Calderón projectors $\mathsf{A}$ Multitrace operator $\mathsf{Id}$, $I_h$ Identity operators $\mathcal{V}$, $\mathsf{V}$, $V_h$ Single layer operators/matrices $\mathcal{K}$, $\mathsf{K}$, $K_h$ Double layer operators/matrices $\mathsf{K}'$, $K_h'$ Adjoint double layer operators/matrices $\mathsf{W}$, $W_h$ Hypersingular operators/matrices $\mathcal{E}$, $\mathsf{E}$, $E_h$ Electric field operators/matrices $\mathcal{H}$, $\mathsf{H}$, $H_h$ Magnetic field operators/matrices

## Functions and spaces

 Symbol(s) Meaning $\mathcal{D}$ The domain of an operator $\mathcal{R}$ The range of an operator $\mathcal{V}$ The dual to the range of an operator Lowercase Greek letters: $\phi$, $\psi$, …Lowercase Roman letters: $u$, $f$, … Scalar valued functions Capital Greek letters: $\Phi$, $\Psi$, …Bold capital Roman letters: $\mathbf{H}$, $\mathbf{E}$, … Vector valued functions Functions with subscripts: $\phi_i$, $\psi_i$, $\Phi_i$, … Basis functions of a discrete space