Configuration | |||
G34 | 1.1244e-02 | 1.7302e-01 | 1.8374e-04 |
GE37 | 7.6288e-04 | 1.5185e-02 | 1.8224e-04 |
This paper concerns the numerical resolution of a data completion problem for the time-harmonic Maxwell equations in the electric field. The aim is to recover the missing data on the inaccessible part of the boundary of a bounded domain from measured data on the accessible part. The non-iterative quasi-reversibility method is studied and different mixed variational formulations are proposed. Well-posedness, convergence and regularity results are proved. Discretization is performed by means of edge finite elements. Various two- and three-dimensional numerical simulations attest the efficiency of the method, in particular for noisy data.
Citation: |
Figure 7.
Ring. QR method. Extension/restriction method. Relative error
Figure 9.
Unit disc. 5% noisy data. RR-QR method. Relative error
Figure 12.
Ring. 5% noisy data. RR-QR method with extension/restriction. Modulus of the error in the approximation of
Table 1.
Unit disc. QR method. Errors for
Configuration | |||
G34 | 1.1244e-02 | 1.7302e-01 | 1.8374e-04 |
GE37 | 7.6288e-04 | 1.5185e-02 | 1.8224e-04 |
Table 2. Ring. QR method. Errors
Configuration | ||||
GExt | 3.9423e-04 | 6.6661e-04 | 6.6661e-04 | 1.7964e-04 |
G34 | 3.5093e-01 | 6.9598e-01 | 4.8011e-01 | 8.1894e-05 |
GE37 | 9.9784e-03 | 3.9068e-02 | 3.8737e-02 | 8.4337e-05 |
Table 3. Ring. QR method. Extension/restriction method. Errors
Configuration | ||||
GExt | 3.7745e-04 | 1.5665e-04 | 1.5665e-04 | 3.1125e-04 |
G34 | 3.4345e-02 | 1.2558e-01 | 8.1477e-03 | 2.6564e-04 |
GE37 | 1.7728e-03 | 1.1968e-02 | 2.9520e-04 | 9.0131e-05 |
Table 4.
Unit disc. 5% noisy data. RR-QR method. Errors in the approximation of
Configuration | ||||
G34 | 3.4698e-02 | 2.9145e-02 | 3.5686e-01 | 7.0667e-03 |
GE37 | 1.8550e-02 | 3.2848e-02 | 1.7154e-01 | 1.1857e-02 |
Table 5.
Ring. 5% noisy data. RR-QR method with extension/restriction. Errors in the approximation of
Configuration | |||||
GExt | 9.2775e-03 | 3.3871e-02 | 4.2425e-03 | 4.2425e-03 | 1.0602e-02 |
G34 | 7.9236e-02 | 3.0600e-02 | 1.5695e-01 | 4.2697e-02 | 8.7901e-03 |
GE37 | 2.6712e-02 | 3.3503e-02 | 7.7043e-02 | 1.6996e-02 | 1.3596e-02 |
Table 6.
Errors in the unit ball of
Domain | |||||
Ball | 1.0834e-01 | 2.3864e-02 | 4.0949e-01 | 2.9336e-03 | |
Ring | 1.2414e-01 | 1.1567e-02 | 2.7969e-01 | 5.6528e-02 | 1.6497e-03 |
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