DPC++ & MPI, buffer, shared memory, variable declare

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I am new to DPC++, and I try to develop a MPI based DPC++ Poisson solver. I read the book and am very confused about the buffer and the pointer with the shared or host memoery. What is the difference between those two things, and what should I use when I develop the code.

Now, I use the buffer initialized by an std::array with const size for serial code and it works well. However when I couple the DPC++ code with MPI, I have to declare a local length for each device, but I fail to do that. Here I attach my code

    define nx 359
    define ny 359
    constexpr int local_len[2];
    global_len[0] = nx + 1;
    global_len[1] = ny + 1;

    for (int i = 1; i < process; i++)
    {
        if (process % i == 0)
        {
            px = i;
            py = process / i;
            config_e = 1. / (2. * (global_len[1] * (px - 1) / py + global_len[0] * (py - 1) / px));
        }
        if (config_e >= cmax)
        {
            cmax = config_e;
            cart_num_proc[0] = px;
            cart_num_proc[1] = py;
        }
    }
    local_len[0] = global_len[0] / cart_num_proc[0];
    local_len[1] = global_len[1] / cart_num_proc[1];
    
    constexpr int lx = local_len[0];
    constexpr int ly = local_len[1];
    queue Q{};
    double *m_cellValue = malloc_shared<double>(size, Q);

I got the error

error: default initialization of an object of const type 'const int[2]'
error: cannot assign to variable 'local_len' with const-qualified type 'const int[2]'
main.cpp:52:18: error: cannot assign to variable 'local_len' with const-qualified type 'const int[2]'

Is there any way to just define a variable size array to do the parallel for in DPC++?

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Victor Eijkhout On BEST ANSWER

You are too eager in using constexpr. Remove all three occurrences in this code, and it should compile. So this has nothing to do with DPC++.