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This paper introduces the concept of Algebraic Electromagnetism to solve the problem of finding stable spatial discretizations of the electromagnetic field for large scale, ultra-wide-band electromagnetic systems, composed of possibly nonlinear subsystems with memory and/or hysteresis effects. It is a thorough approach to exact discrete electromagnetism, given by an algebraic construction of general...
This paper presents a transformation of Maxwell's equations for general nonlinear material operators into a system state equation of an equivalent nonlinear distributed parameter system. The proposed formulation has a fair amount of practical and didactic advantages, with regard to modeling hysteresis and memory effects, understanding causality, control and stability of electromagnetic fields, formulating...
To computationally tackle electromagnetic system security problems, a general new approach for obtaining exact ordinary differential equation system representations of Maxwell's equations is presented. The approach is compatible with a huge class of general non-linear material operators and emphasis is put on the problem of unauthorized control. This problem is modelled at the physical representation...
This paper introduces a new matrix assembly algorithm for nonlinear problems that decomposes the problem into parts that are well suited for parallel computation on GPGPUs. It has the strength that recomputations in nonlinear entries of the stiffness matrices are embarrassingly parallel. The algorithm is used to solve electro-quasistatic problems. The proposed discretization includes the handling...
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