1. About electromagnetic general purpose AE method theory robust finite element of frequency response

The electromagnetic vector A method and electric field E method of Maxwell's electromagnetic field equations are equivalent formulations, so we have theoretically integrated them into the electromagnetic general-purpose AE hybrid method. We will explain the history and main points of the development of electromagnetic general-purpose AE method theory.

1) Spurious error of electromagnetic A normal finite element patch test

Spurious errors in finite element patch testing of electromagnetic A-normal elements are caused by the side element formulation. The electric field preserving nodal elements of the electromagnetic general-purpose AE method, the electromagnetic A method and the electric field E method, have confirmed the inherent characteristics of the elements according to Maxwell's electromagnetic field theory. Electromagnetic A normal element error requires drastic countermeasures using the electromagnetic general-purpose AE method.

2) Electromagnetic general-purpose AE method robust nodal finite element with electric field conservation

Spurious errors in side finite element patch tests can be resolved using the robust nodal finite element electromagnetic general-purpose AE method with electric field conservation.

3) Summary of electromagnetic general-purpose AE hybrid method theory

Using the electromagnetic general-purpose AE method using the electromagnetic vector A method and the electric field E method, we have developed and verified a finite element method of the electric field conservation divergence theorem that can rigorously analyze Maxwell's simultaneous electromagnetic equations. The electromagnetic general-purpose AE method, electromagnetic A method and electric field E method, give the same analysis results. The spurious error of the electromagnetic A normal element is caused by the spurious integral compound error that assumes a constant distribution A in the side element formulation, although the side tangential electromagnetic A(s) of the Stokes theorem that preserves the electromagnetic A is a linear interpolation distribution. . In the electromagnetic field general-purpose AE method, the electric field, charge, and magnetic flux conservation equations of Maxwell's equations are strictly constrained by the divergence theorem and the undetermined multiplier method.

4) Electromagnetic general-purpose AE method Electromagnetic resistivity physical exploration using electric field conservation finite elements and optimal design of electromagnetic equipment

The electromagnetic general-purpose AE method electric field conservation finite element can accurately calculate the resistivity sensitivity of electric and magnetic fields, making it possible to perform innovative underground electromagnetic exploration of the underground hydrological structure of volcanoes and earthquake source areas. For example, it is said that 90 tons of contaminated water will be generated per day at Fukushima II, but fundamental countermeasures can be planned and implemented through electromagnetic and physical surveys of the groundwater geological structure. Since electric and magnetic field sensitivities can be precisely calculated, it becomes possible to optimally design electromagnetic devices such as motors.

The electromagnetic general-purpose AE method's electromagnetic A legal formula and electric field E legal formula's frequency equation of motion and the undetermined multiplier method with electric field and charge conservation constraints yield the same analysis results that are equivalent to Maxwell's electromagnetic field theory. The electromagnetic general-purpose AE method provides the same analysis results for exact analysis of AC electromagnetic field response using both the electromagnetic A legal formula and the electric field E legal formula.