Method using an appropriately programmed computer or an appropriately designed computing device for determining an electromagnetic near-field of a field excitation source of an electrical system, in particular for analysis and/or optimization of antenna radiation, of a crosstalk problem, of signal reflection/transmission, of a stray field, of an irradiation problem or the like, inside a domain under consideration comprising the system and split into N -partitions, comprising the steps: - defining electric and magnetic properties of the material distribution of the system in each partition inside the domain under consideration; - defining at least one field excitation source inside the system; - determining the electromagnetic near-field components inside at least one and in particular all partitions by solving the Maxwell's equations of the near-field, taking into account the defined material distribution and the defined field excitation source, where a discontinuous Galerkin formulation (DG-FEM formulation) of the near-field problem is used to solve the Maxwell's equations, characterized in that the applications of mass operator, curl operator and trace operator necessary for computing the spatial and/or time derivative to the near-field component exhibit a determination effort linear to the number N of partitions of the domain under consideration and to the number M of the test functions P i used in the linear position, where each near-field component of each partition is represented as v x = ∑ i = 0 M - 1 v i ⁢ P i x by a linear position of M predetermined and holonomic test functions P i orthogonal to one another in respect of a scalar product and weighted with field coefficients v i, where a spatial derivative of the near-field component is represented as grad v x = ∑ i = 0 M - 1 v i ⁢ grad P i x = ∑ i = 0 M - 1 w i ⁢ P i x as a linear position of these test functions P i weighted with derivative coefficients w i, and where each coefficient w i is calculated by w i = f ( v j, w j) with linear effort recursively from a quantity of field coefficients v i and previously determined derivative coefficients w j. - defining electric and magnetic properties of the material distribution of the system in each partition inside the domain under consideration; - defining at least one field excitation source inside the system; - determining the electromagnetic near-field components inside at least one and in particular all partitions by solving the Maxwell's equations of the near-field, taking into account the defined material distribution and the defined field excitation source, where a discontinuous Galerkin formulation (DG-FEM formulation) of the near-field problem is used to solve the Maxwell's equations, characterized in that the applications of mass operator, curl operator and trace operator necessary for computing the spatial and/or time derivative to the near-field component exhibit a determination effort linear to the number N of partitions of the domain under consideration and to the number M of the test functions P i used in the linear position, where each near-field component of each partition is represented as v x = ∑ i = 0 M - 1 v i ⁢ P i x by a linear position of M predetermined and holonomic test functions P i orthogonal to one another in respect of a scalar product and weighted with field coefficients v i, where a spatial derivative of the near-field component is represented as grad v x = ∑ i = 0 M - 1 v i ⁢ grad P i x = ∑ i = 0 M - 1 w i ⁢ P i x as a linear position of these test functions P i weighted with derivative coefficients w i, and where each coefficient w i is calculated by w i = f ( v j, w j) with linear effort recursively from a quantity of field coefficients v i and previously determined derivative coefficients w j.