Modify interpolation scheme

[t-young31]

Overhaul interpolation from the split grid to the central grid.

1. Different scheme required for each field component.
2. Is implemented for the electric field, although interpolateTimeDomainFieldCentralEBandLimited was hacked to work for the 2D case, this should be checked.
3. More significant work required for the magnetic field
4. Enable interpolation to be performed right up to the edge of the computational domain.

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Dependencies:

• Theoretical outline from @prmunro

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Tasks specified in PSTD_interpolation_scheme.pdf:

• Write (time-domain) interpolation methods for E-field components. Should use BLi, and if not possible, fall back on cubic interpolation. Closed by Band Limited Interpolation Functionality #62.
• Write (time-domain) interpolation methods for H-field components using the 2D-method interpolation method. Interpolation in each dimension should again use BLi if possible, and failing that fall back on cubic. Closed by Band Limited Interpolation Functionality #62.
• Write interpolation methods for the E- and H- fields in the frequency domain. Compared to the time-domain, this scheme must be able to handle complex data. #112
• Unit tests for cubic interpolation methods. Closed by Band Limited Interpolation Functionality #62.
• Unit tests for BLi interpolation methods. #111
• Unit tests for interpolate{TimeDomain,FrequencyDomain}{E,H}{x,y,z} functions. #110
• fieldsample does not allow for extraction of magnetic field at the vertices - this must be added. #109
• Change the interpolation calls in exphasorssurface, exphasorsvolume, and fieldsample to the new interpolation functions. #113
• Check if using the PML values of E and H improve the interpolation. Simple exponential-attenuated test case #114
• Remove now-redundant functions (and headers). #115

[giordano]

Now done!

Related to interpolation, there are many interpolation functions which are supposed to return int, but the return value is never actually used. For example

TDMS/tdms/src/interpolate.cpp

Line 1086 in 805e5dd

int mxInterpolateFieldCentralH_TM( mxArray *Hx_yee , mxArray *Hy_yee , mxArray *Hz_yee,

can return -1 under certain conditions

TDMS/tdms/src/interpolate.cpp

Lines 1094 to 1096 in 805e5dd

	if( mxGetNumberOfDimensions(Hx_yee) != 2){
	fprintf(stderr,"Error in mxInterpolateFieldCentralH_TM, Ex_yee does not have 3 dimensions\n");
	return -1;

but its use at

TDMS/tdms/src/tdms_iterator.cpp

Lines 6174 to 6176 in 805e5dd

	mxInterpolateFieldCentralH_TM( plhs[3] , plhs[4] , plhs[5],
	&plhs[16] ,&plhs[17] , &plhs[18],
	2, pind_iu - pind_il - 1, 2, pind_ju - pind_jl - 1, 0, 0);

doesn't check the return value, so that an error would never be caught.

I guess these functions should either be void and throw errors when needed, or at very least the return values should be checked and appropriately dealt with.

[samcunliffe]

Closing as this as done: #44 can stay open until someone with research time wants to take it on, and #109 will be addressed independently.