论文标题
弦分解用于光谱变形
Chordal Decomposition for Spectral Coarsening
论文作者
论文摘要
我们介绍了一个新颖的求解器，以显着降低几何操作员的大小，同时以最低频率保留其光谱特性。我们使用和弦分解来制定凸优化问题，该问题使用户可以控制操作员的稀疏模式。这允许在操作员的光谱准确性与应用成本之间进行权衡。我们通过变量的变化有效地最大程度地减少了能量，并在光谱变形时实现了最新的结果。我们的求解器进一步启用了新的应用程序，包括音量到地面近似，并从网格中脱离操作员，即，一个人可以生成网格式型号以进行可视化，并分别优化运算符进行计算。
We introduce a novel solver to significantly reduce the size of a geometric operator while preserving its spectral properties at the lowest frequencies. We use chordal decomposition to formulate a convex optimization problem which allows the user to control the operator sparsity pattern. This allows for a trade-off between the spectral accuracy of the operator and the cost of its application. We efficiently minimize the energy with a change of variables and achieve state-of-the-art results on spectral coarsening. Our solver further enables novel applications including volume-to-surface approximation and detaching the operator from the mesh, i.e., one can produce a mesh tailormade for visualization and optimize an operator separately for computation.
