Notation

Posted on 2017-07-162017-09-28 by The Bempp Team

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