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Heat Equation 2D Bug Fixes #2384

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Sep 18, 2024
Merged

Heat Equation 2D Bug Fixes #2384

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4 changes: 2 additions & 2 deletions example/heatEquation2D/src/analyticalSolution.hpp
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Original file line number Diff line number Diff line change
Expand Up @@ -39,14 +39,14 @@ auto validateSolution(
double maxError = 0.0;
for(uint32_t j = 1; j < extent[0] - 1; ++j)
{
for(uint32_t i = 0; i < extent[1]; ++i)
for(uint32_t i = 1; i < extent[1] - 1; ++i)
{
auto const error = std::abs(buffer.data()[j * extent[1] + i] - exactSolution(i * dx, j * dy, tMax));
maxError = std::max(maxError, error);
}
}

constexpr double errorThreshold = 1e-5;
constexpr double errorThreshold = 1e-4;
return std::make_pair(maxError < errorThreshold, maxError);
}

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10 changes: 6 additions & 4 deletions example/heatEquation2D/src/heatEquation2D.cpp
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Expand Up @@ -55,16 +55,17 @@ auto example(TAccTag const&) -> int
constexpr alpaka::Vec<Dim, Idx> haloSize{2, 2};
constexpr alpaka::Vec<Dim, Idx> extent = numNodes + haloSize;

constexpr uint32_t numTimeSteps = 100;
constexpr double tMax = 0.001;
constexpr uint32_t numTimeSteps = 4000;
constexpr double tMax = 0.1;

// x, y in [0, 1], t in [0, tMax]
constexpr double dx = 1.0 / static_cast<double>(extent[1] - 1);
constexpr double dy = 1.0 / static_cast<double>(extent[0] - 1);
constexpr double dt = tMax / static_cast<double>(numTimeSteps);

// Check the stability condition
constexpr double r = dt / std::min(dx * dx, dy * dy);
if constexpr(r > 0.5)
double r = 2 * dt / ((dx * dx * dy * dy) / (dx * dx + dy * dy));
if(r > 1.)
{
std::cerr << "Stability condition check failed: dt/min(dx^2,dy^2) = " << r
<< ", it is required to be <= 0.5\n";
Expand Down Expand Up @@ -169,6 +170,7 @@ auto example(TAccTag const&) -> int
#ifdef PNGWRITER_ENABLED
if((step - 1) % 100 == 0)
{
alpaka::wait(computeQueue);
alpaka::memcpy(dumpQueue, uBufHost, uCurrBufAcc);
alpaka::wait(dumpQueue);
writeImage(step - 1, uBufHost);
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8 changes: 7 additions & 1 deletion example/heatEquation2D/src/writeImage.hpp
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Expand Up @@ -8,6 +8,7 @@

#include <pngwriter.h>

#include <cmath>
#include <cstdint>
#include <iomanip>
#include <sstream>
Expand All @@ -31,7 +32,12 @@ auto writeImage(uint32_t const currentStep, T_Buffer const& buffer) -> void
for(uint32_t x = 0; x < extents[1]; ++x)
{
auto p = buffer.data()[y * extents[1] + x];
png.plot(x + 1, extents[0] - y, p, 0., 1. - p);
png.plot(
x + 1,
extents[0] - y,
2 * std::exp(std::sqrt(p)) / std::exp(std::sqrt(2)) - 1,
0.4,
2 - 2 * std::exp(std::sqrt(p)) / std::exp(std::sqrt(2)));
}
}
png.close();
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