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