Why would an Aparapi Kernel running on a AMD GPU allow very large @Local arrays, but not with Nvidia?

Question

I have a Java program that needs access to a large array from the GPU's local memory. I can declare and access a large array with a '@Local float[] mem = new float[1000000];' using Aparapi on a laptop with an AMD Radeon GPU and it works just fine, but when I try the same thing on a laptop with an Nvidia GeForce 1660 Ti I get an out of resources error from OpenCl. The Nvidia card has 3 Gigs of shared memory so I thought it should have no problem, but obviously not.

I have been searching for a solution to the problem with Google for a few hours now, but I am unable to find any relevant documents.

Here's the code that initializes the kernel memory:

public class MemoryKernel extends Kernel {

    /** Working memory - each worker gets its own individual area of fixed memory.  It is 
     * protected so that the test cases can access it. */
    @Local protected final float[] mem;


    /** Memory size in blocks  */
    final int memSize;

    /** Size of a block of memory */
    final int blockSize;

    /** Number of worker items */
    int workGroupSize;

    /** A small buffer for testing purposes */
    final float[] buf;

    public MemoryKernel(int blockSize, int memSizeInBlocks, int workGroupSize) {
        this.memSize = memSizeInBlocks;
        this.blockSize = blockSize;
        // A typical initialisation is 17 * 50 * 1000
        mem = new float[memSizeInBlocks * blockSize * workGroupSize];
        initMem(workGroupSize);

        // A small buffer accessed only by the test cases in the gputrace.test package for testing
        // the ray tracer's functions
        buf = new float[blockSize];
        setExplicit(true);
        put(buf);
    }
...