  Liquid Argon Time Projection Chamber (LArTPC) technology is commonly utilized
in neutrino detector designs. It enables detailed reconstruction of neutrino
events with high spatial precision and low energy threshold. Its field response
(FR) model describes the time-dependent electric currents induced in the
anode-plane electrodes when ionization electrons drift nearby. An accurate and
precise FR is a crucial input to LArTPC detector simulations and charge
reconstruction. Established LArTPC designs have been based on parallel wire
planes. It allows accurate and computationally economic two-dimensional (2D) FR
models utilizing the translational symmetry along the direction of the wires.
Recently, novel LArTPC designs utilize electrodes formed on printed circuit
board (PCB) in the shape of strips with through holes. The translational
symmetry is no longer a good approximation near the electrodes and a new FR
calculation that employs regions with three dimensions (3D) has been developed.
Extending the 2D models to 3D would be computationally expensive. Fortuitously,
the nature of strips with through holes allows for a computationally economic
approach based on the finite-difference method (FDM). In this paper, we present
a new software package "pochoir" that calculates LArTPC field response for
these new strip-based anode designs. This package combines 3D calculations in
the volume near the electrodes with 2D far-field solutions to achieve fast and
precise field response computation. We apply the resulting FR to simulate and
reconstruct samples of cosmic-ray muons and $^{39}$Ar decays from a Vertical
Drift (VD) detector prototype operated at CERN. We find the difference between
real and simulated data within 5 %. Current state-of-the-art LArTPC software
requires a 2D FR which we provide by averaging over one dimension and estimate
that variations lost in this average are smaller than 7 %.
