General comments:

In this paper, the authors are interested in studying and improving the performance of high resolution, continental scale ice-sheet modeling by leveraging pseudo-transient continuation and GPU hardware. An unstructured, finite-element code is developed in CUDA C to solve the momentum balance with the Shallow Shelf approximation (named FastIceFlo v1.0). The code is tested on two regional-scale glaciers. The scalability and wall time of the solver is reported and analyzed using a fixed resource set of 1 GPU and increasing problem size. This is compared to ISSM's CG iterative solver on 36 CPU cores.

The paper is well-written, and the methodology is unique enough with respect to ice-sheet modeling to warrant publication after a minor revision. The paper shows that the FastIceFlo solver is faster than ISSM's CG solver in most cases for the specified case study showing that it is possible to use pseudo-transient continuation and GPUs to improve performance. I'm not satisfied with the price and power consumption comparisons, and I think these sections should be strengthened or omitted. I also think that a profiler tool should be used to verify the low memory throughputs reported as this would help clarify future directions and better inform readers about the potential of the methods.

Specific comments:

 - Line 37: The authors state, "...the traditional way of solving the governing equations of ice-sheet flow, such as the finite-element analysis, is not adapted to GPUs as they cannot handle large sparse matrices and linear solvers." GPUs can handle large sparse linear solvers. There are vender specific libraries such as cuSolverSP. For multi-GPU iterative solvers see PETSc, Trilinos and Hypre.

 - Lines 213-215: The authors state, "...the power consumption of the PT GPU implementation was approximately one-seventh of the traditional CPU implementation..." This comparison is misleading. A V100 GPU also requires a CPU which consumes power. One would need to include the power of the CPU for a fair comparison. A variation of this statement is also in the abstract (lines 13-14) and conclusion (line 271).

 - Line 230: Where are L1TEX and L2 cache reported from?

 - Lines 235-236: Where are the peak memory throughputs reported from? Was this an additional study performed?

 - Lines 238-240: 3-4% of measured peak memory throughput is very low and would indicate a latency bound kernel. These numbers should be verified with a profiler such as nvprof or nsight.

Technical comments:

 - Equation 2: epsilons should be defined

 - Equation 14: not on the same line

 - Equation 14: epsilon_w should be defined. Should this be Delta w?

 - Figure 2: It would be good to also show the meshes used in the study to better understand the mesh quality.

 - Line 187: "performance of PT" should be "performance of the PT"

 - Line 200: The values for the damping parameter, nonlinear viscosity relaxation scalar and transient pseudo time step are not provided for the study.

 - Line 207: References are required for the price values of the Tesla V100 GPU and Xeon Gold 6140 CPU used in this study. A comparison between the prices is also written in the abstract (lines 12-13) and conclusion (line 270). References should be added there as well.

 - Line 209: It would be good to have a reference for the NVIDIA System Management Interface used in this study and a version number.

 - Line 211: A reference is also required for the hardware specification sheet used to acquire the thermal design power of the Intel Xeon Gold 6140 processor.

 - Lines 219-222: A table or graph of speedups would help highlight the values obtained in the study.

See attachment