Resistive heating solver

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The re­sis­tive heat­ing solver is a sim­pli­fied ver­sion of the ed­dy cur­rent mod­el where on­ly re­sis­tive and no in­duc­tive ef­fects are com­put­ed. The vec­tor po­ten­tial A is equal to ze­ro all over and on­ly the scalar po­ten­tial φ is kept. This way, the dif­fu­sion of the EM fields is not solved. The cur­rent den­si­ty is pro­por­tion­al to the gra­di­ent of the scalar po­ten­tial, which cor­re­sponds to a uni­form cur­rent. There are no in­duc­tive ef­fects since A=0, hence no cou­pling from a coil to the work­piece. This mod­el is for very slow ris­ing cur­rents in a piece con­nect­ed to a gen­er­a­tor, where the dif­fu­sion and in­duc­tive ef­fects can be con­sid­ered as in­fi­nite­ly fast. The joule heat­ing due to the cur­rent is still tak­en in­to ac­count. Very large timesteps can be used and since A = 0 and no BEM is need­ed, this makes this solver much faster than the full ed­dy cur­rent mod­el.