The finite element method is applied in the time domain to establish formulations for the integration of second-order and hyperbolic (dynamic) problems. Modal decomposition in the space domain is used to recover the well-established method for uncoupling the equations of motion, which is extended to include general time approximation bases. The limitations of this approach in the implementation...

In this paper the possibility of applying the Trefftz-method to thick and thin shells is discussed. A mixed variational formulation is used in which the assumed strain and stress functions are derived from the three-dimensional solution representation for the displacement field. For the construction of the linearly independent Trefftz trial functions both the Neuber/Papkovich solution represent...

The effective permeability of electromagnetic metamaterials can deviate significantly from unity at high frequencies – an intriguing property not available in natural materials. However, we show both analytically and numerically that this artificial magnetism has limitations: the stronger the magnetic response, the less accurate the homogenization. New computational aspects of the paper include...

A general symmetric Trefftz Discontinuous Galerkin method is built for solving the Helmholtz equation with piecewise constant coefficients. The construction of the corresponding local solutions to the Helmholtz equation is based on a boundary element method. A series of numerical experiments displays an excellent stability of the method relatively to the penalty parameters, and more importantly...

In Trefftz discontinuous Galerkin methods a partial differential equation is discretized using shape functions that are chosen to be elementwise in the kernel of corresponding operator. We propose new variant, embedded method, which projection an underlying method onto subspace Trefftz-type. The can described very general way and obtain it no have calculated explicitly, instead embedding operat...

Trefftz methods are finite element-type schemes whose test and trial functions are (locally) solutions of the targeted differential equation. They are particularly popular for time-harmonic wave problems, as their trial spaces contain oscillating basis functions and may achieve better approximation properties than classical piecewise-polynomial spaces. We review the construction and properties ...