stovetop grilling

Grilling on induction cooktop

I've just remodelled my kitchen with an induction cooktop and am cautiously collecting my new cooking equipment. Will one of those small Japanese stovetop grills work on this type of cooktop? I am unclear as to whether it is the grill surface or the heat from below that cooks food on regular cooktops. I was not successful with using a stovetop grill on my old electric cooktop.
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