Motivated by Chow-Luo's combinatorial Ricci flow on surfaces and Luo's combinatorial Ricci flow on compact 3-manifolds with boundary, we introduce combinatorial Calabi flow for decorated hyperbolic polyhedral metrics on 3-manifolds with toroidal boundary to find complete hyperbolic metrics. Dual to Casson and Rivin's approach to solve Thurston's gluing equation by maximizing the volume function for angle structures, the combinatorial Calabi flow on 3-manifolds with toroidal boundary works on decorated hyperbolic polyhedral metrics to ensure that there is no shearing around the edges and finds the complete hyperbolic metric by minimizing the combinatorial Calabi energy. Basic properties of combinatorial Calabi flow on 3-manifolds with toroidal boundary are established. The most important ones include that the equilibrium points of the combinatorial Calabi flow correspond to complete hyperbolic metrics on 3-manifolds with toroidal boundary and the local convergence of the combinatorial Calabi flow. We also study the combinatorial Calabi flow on an ideal tetrahedron. It is shown that for any prescribed admissible dihedral angles, the solution of combinatorial Calabi flow on an ideal tetrahedron exists for all time and converges exponentially fast to a complete hyperbolic polyhedral metric with the prescribed dihedral angles.

受Chow-Luo在曲面上的组合Ricci流和Luo在带边界的紧型3流形上的组合Ricci流的激励，我们引入了组合式Calabi流，用于在具有环形边界的3流形上装饰双曲多面体度量，以找到完整的双曲度量。与Casson和Rivin的方法（通过最大化角度结构的体积函数）来解决Thurston的胶粘方程式双重，具有环形边界的3流形上的组合Calabi流在修饰的双曲多面体度量上起作用，以确保在边缘没有剪切，并找到通过最小化组合式Calabi能量来完成双曲度量。建立了具有环形边界的三流形上组合卡拉比流的基本性质。最重要的是，组合卡拉比流的平衡点对应于具有环形边界的3流形上的完整双曲度量，并且组合卡拉比流的局部收敛。我们还研究了理想四面体上的组合卡拉比流。结果表明，对于任何规定的容许二面角，理想的四面体上的组合卡拉比流解一直存在，并且以指数方式快速收敛到具有规定二面角的完整双曲多面体度量。