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It seems that "LinearSolveMethod" -> {"Pardiso"} is not available on the Raspberry Pi 3 version (10.3, 32-bit Linux, ARM) of Mathematica. Is there a package that can be loaded to use Pardiso or an alternate method with the same accuracy and memory efficiency?

It's being used with "FiniteElement" in NDSolve.

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I would guess probably not, unless WRI chooses to integrate PARDISO on the ARM platform. It comes "for free" with Intel MKL, which is used on all the other platforms. They could replace it with a collection of other packages, but I guess it's easier to just leave some features unsupported rather than to find replacements for all of the MKL functionality, especially considering that Raspberry Pi isn't meant for high performance anyway. Of course you can compile PARDISO yourself and then call it using LibraryLink, but that won't be integrated with NDSolve.

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